Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Jakub Duda
by Dale Alspach 02 Aug '06

02 Aug '06

This is an announcement for the paper "On Gateaux differentiability of pointwise Lipschitz mappings" by Jakub Duda. Abstract: We prove that for every function $f:X\to Y$, where $X$ is a separable Banach space and $Y$ is a Banach space with RNP, there exists a set $A\in\tilde\mcA$ such that $f$ is Gateaux differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the set of points where $f$ is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every $K$-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to $\tilde\mcC$; this improves a result due to Borwein and Wang. Another corollary is that if $X$ is Asplund, $f:X\to\R$ cone monotone, $g:X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is Hadamard differentiable and $g$ is Frechet differentiable. Archive classification: Functional Analysis Mathematics Subject Classification: 46G05; 46T20 Remarks: 11 pages; updated version The source file(s), ongatdif.tex: 43273 bytes, is(are) stored in gzipped form as 0511565.gz with size 13kb. The corresponding postcript file has gzipped size 61kb. Submitted from: jakub.duda(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0511565 or http://arXiv.org/abs/math.FA/0511565 or by email in unzipped form by transmitting an empty message with subject line uget 0511565 or in gzipped form by using subject line get 0511565 to: math(a)arXiv.org.

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Abstract of a paper by Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai and Alicja Szymaszkiewicz
by Dale Alspach 02 Aug '06

02 Aug '06

This is an announcement for the paper "Basic topological and geometric properties of Cesaro--Orlicz spaces" by Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai and Alicja Szymaszkiewicz. Abstract: Necessary and sufficient conditions under which the Cesaro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesaro--Orlicz spaces $\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\cfi$ are given. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 46B45, 46E30 Remarks: 16 pages The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes, pm2563new.tex: 46836 bytes, is(are) stored in gzipped form as 0607730.tar.gz with size 23kb. The corresponding postcript file has gzipped size 55kb. Submitted from: Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai and Alicja Szymasz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0607730 or http://arXiv.org/abs/math.FA/0607730 or by email in unzipped form by transmitting an empty message with subject line uget 0607730 or in gzipped form by using subject line get 0607730 to: math(a)arXiv.org.

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Abstract of a paper by Erwin Lutwak, Deane Yang, and Gaoyong Zhang
by Dale Alspach 02 Aug '06

02 Aug '06

This is an announcement for the paper "Volume inequalities for isotropic measures" by Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Abstract: A direct approach to Ball's simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe's characterization of the simplex for Ball's inequality and extends it from discrete to arbitrary measures. It also yields the dual inequality, along with equality conditions, and it does both for arbitrary measures. Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 52A40 Remarks: 10 pages, to appear in American Journal of Mathematics The source file(s), bb2_copy7.tex: 32473 bytes, is(are) stored in gzipped form as 0607753.gz with size 10kb. The corresponding postcript file has gzipped size 45kb. Submitted from: dyang(a)poly.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0607753 or http://arXiv.org/abs/math.MG/0607753 or by email in unzipped form by transmitting an empty message with subject line uget 0607753 or in gzipped form by using subject line get 0607753 to: math(a)arXiv.org.

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Abstract of a paper by Oscar Valero
by Dale Alspach 02 Aug '06

02 Aug '06

This is an announcement for the paper "Quotient normed cones" by Oscar Valero. Abstract: Given a normed cone $(X,p)$ and a subcone $Y,$ we construct and study the quotient normed cone $(X/Y,\tilde{p})$ generated by $Y$. In particular we characterize the bicompleteness of $(X/Y,\tilde{p})$ in terms of the bicompleteness of $(X,p),$ and prove that the dual quotient cone $((X/Y)^{*},\|\cdot \|_{\tilde{p},u})$ can be identified as a distinguished subcone of the dual cone $(X^{*},\|\cdot \|_{p,u})$. Furthermore, some parts of the theory are presented in the general setting of the space $CL(X,Y)$ of all continuous linear mappings from a normed cone $(X,p)$ to a normed cone $(Y,q),$ extending several well-known results related to open continuous linear mappings between normed linear spaces. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: 54E35; 54E50; 54E99; 54H11 Remarks: 17 pages The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes, pm2745new.tex: 58553 bytes, is(are) stored in gzipped form as 0607619.tar.gz with size 26kb. The corresponding postcript file has gzipped size 61kb. Submitted from: o.valero(a)uib.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0607619 or http://arXiv.org/abs/math.FA/0607619 or by email in unzipped form by transmitting an empty message with subject line uget 0607619 or in gzipped form by using subject line get 0607619 to: math(a)arXiv.org.

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SUMIRFAS schedule
by Bill Johnson 28 Jul '06

28 Jul '06

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Metric Geometry Concentration Week at A&M
by Bill Johnson 13 Jul '06

13 Jul '06

The Concentration Week on "Metric Geometry and Geometric Embeddings of Discrete Metric Spaces" will begin with registration at 9:00 AM on Monday, July 17, and end in the early afternoon on Saturday, July 22. All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 155. Registration and Reimbursement. Please register at the registration desk in Blocker when you arrive on Monday or Tuesday. Most participants will have their rooms direct billed to the Mathematics Department. If you are to receive a meal allowance, please fill out the reimbursement sheet given you at the registration desk with your name, social security number (if you have one), and the address to which you want the reimbursement check sent. Sign at the bottom of the form above "Traveler Signature" and check the appropriate box on that line. If you are not a U. S. resident, please give Cara your passport to be photocopied. Banquet. The Concentration Week banquet will be at 6:00 PM Thursday, July 20 at Cafe Eccell, http://www.cafeeccell.com/, 101 Church Ave. (also called Church St.), at the intersection of Church Ave. with Wellborn Road. Church Ave. is one block north of University Dr; it is an easy walk to the restaurant from Blocker. For technical reasons we must charge a registration fee of $15 per person for the banquet on Thursday, which can be paid when you register for the Concentration Week. At registration please indicate which entree (chateau loin filet, grilled chicken breast, voodoo salmon, or vegetarian) you prefer. If you will arrive after Tuesday, please email Cara, cara(a)math.tamu.edu, if you (and a companion, if applicable) will come to the banquet, because Cara must give the restaurant the number of diners in advance. Airport pick up. If you are staying at Hampton Inn, you can request a shuttle from Hampton Inn upon arrival at Easterwood Airport from the phone near the car rental desks. Alternatively, you can call the Hampton Inn at (979) 846-0184 before boarding your flight to tell them your arrival time. If you are staying elsewhere, you can ask Cara to book University Taxi. Please give Cara your arrival time and flight number. University Taxi will bill the Mathematics Department. Give the driver, usually Mr. Yimmy, your name and tell him you are attending Professor Johnson's Workshop. The 800 for University Taxi is 1-888-377-4300. Parking. You can park in the Northside Garage across the street from Blocker for $8/day if space is available. Entering and leaving the NSG is a pain and we suggest that instead you park in the Northgate Parking Garage near Church St. at 309 College Main St. for $3/day. Informal discussion. Blocker 627 and 628 can be used for informal discussions. We also have Milner 317 http://www.tamu.edu/map/building/overview/MILN.html reserved for Workshop activities, and other open rooms in Milner can be used. Computer access. Will be available in Blocker during designated hours. Please sign up at the registration desk. Also, all hotels have wireless Internet access. For security reasons TAMU does not offer wireless Internet access to visitors. Visual aids. Blocker 165 contains equipment for overhead transparency presentations, lap top attachments for power point (or the like) presentations, and white boards. Schedule. The schedule below is subject to change. We expect that "impromptu" talks will be added. Talks designed to introduce non experts and graduate students to aspects of metric geometry are mark with a *. All talks will be in Blocker 165 Note that there will be time between talks for run-over, questions, and discussion. Monday, July 17. 9:00- 9:30 Coffee, Blocker 155, & Registration in Blocker 9:30-10:20 Assaf Naor, *A survey of definitions, results and techniques in metric embedding theory, I* 10:40-11:00 Coffee and registration. 11:00-12:00 Guoliang Yu, *The Novikov conjecture and metric geometry* 12:15- 1:55 Lunch (there are a number of restaurants in the Northgate/Church Ave. area.) 1:55- 2:45 Assaf Naor, *A survey of definitions, results and techniques in metric embedding theory, II* 3:10- 4:00 Yuval Peres, Markov chains, martingales and metric embedding 4:20- Informal discussions Tuesday, July 18 9:00- Coffee, Blocker 155 9:30-10:20 Moses Charikar, *Metric Embeddings in Combinatorial Optimization* 10:45-11:45 Piotr Indyk, *Low-distortion embeddings and data structures* 12:00- 1:40 Lunch break 1:40- 2:30 Sanjeev Arora, Local versus Global phenomena and their importance in approximation algorithms 2:50- 3:15 Yury Makarychev, Directed Metrics and MIN 2CNF Deletion 3:30- 3:55 Konstantin Makarychev, Directed Metrics and Directed Graph Partitioning Problems 4:10- Informal discussions Wednesday, July 19 9:00- Coffee, Blocker 155 9:30-10:20 Bruce Kleiner, BiLipschitz embeddings of metric spaces in Banach spaces 10:40-11:10 Marianna Csornyei, Sard's theorem revisited 11:30-12:00 Leonid Kovalev, Examples of Embeddings via dynamical systems 12:20- 2:00 Lunch break 2:00- 2:50 Robert Krauthgamer, On embedding edit distance into l_1 3:10- 3:50 Yuri Rabinovich, Hard Metric from Abelian Groups 4:10- 5:00 Adi Shraibman, Margins of concept classes 5:15- Informal discussions Thursday, July 20 (Note late starting time) 9:30- Coffee, Blocker 155 10:10-11:00 Gideon Schechtman, Planar transportation cost space is not in $L_1$ 11:20-12:00 Nir Y Ailon, The Fast Johnson-Lindenstrauss Transform with Applications 12:20- 3:00 Lunch break 3:00- 3:50 James Lee, Mixed-norm embeddings and vertex isoperimetry 4:20- 5:10 Avner Magen, Integrality gaps of SDP for Vertex Cover and relations to $\ell_1$ embeddability of negative type metrics Friday, July 21 9:00- Coffee, Blocker 155 9:30-10:20 Ofer Neiman, Advances in metric embedding theory 10:40-11:30 Manor Mendel, Ramsey partitions and proximity data-structures 11:50- 1:30 Lunch break 1:30- 3:30+ Problem Session (Sanjeev Arora, moderator) 3:40- Informal discussions Saturday, July 22 9:30- Coffee, Blocker 155 10:00-10:50 Piotr Nowak, Property A 11:10-12:00 Assaf Naor, Chaining on metric spaces

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Abstract of a paper by E. Ournycheva and B. Rubin
by Dale Alspach 11 Jul '06

11 Jul '06

This is an announcement for the paper "Composite cosine transforms" by E. Ournycheva and B. Rubin. Abstract: The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting mathematical object useful for applications. We introduce more general integral transforms that reveal distinctive features of higher-rank objects in full generality. We call these new transforms the composite cosine transforms, by taking into account that their kernels agree with the composite power function of the cone of positive definite symmetric matrices. We show that injectivity of the composite cosine transforms can be studied using standard tools of the Fourier analysis on matrix spaces. In the framework of this approach, we introduce associated generalized zeta integrals and give new simple proofs to the relevant functional relations. Our technique is based on application of the higher-rank Radon transform on matrix spaces. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 42B10; Secondary 52A22 Remarks: 15 pages The source file(s), ctb12.tex: 51867 bytes, is(are) stored in gzipped form as 0607224.gz with size 18kb. The corresponding postcript file has gzipped size 80kb. Submitted from: ournyche(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0607224 or http://arXiv.org/abs/math.FA/0607224 or by email in unzipped form by transmitting an empty message with subject line uget 0607224 or in gzipped form by using subject line get 0607224 to: math(a)arXiv.org.

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Abstract of a paper by Jorge Galindo
by Dale Alspach 10 Jul '06

10 Jul '06

This is an announcement for the paper "On unitary representability of topological groups" by Jorge Galindo. Abstract: We prove that the additive group $(E^\ast,\tau_k(E))$ of an $\mathscr{L}_\infty$-Banach space $E$, with the topology $\tau_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is \emph{unitarily representable}). This is the same as proving that the topological group $(E^\ast,\tau_k(E))$ is uniformly homeomorphic to a subset of $\ell_2^\kappa$ for some $\kappa$. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative $C^\ast$-algebras are unitarily representable in the topology of uniform convergence on compact subsets. The unitary representability of free locally convex spaces (and thus of free Abelian topological groups) on compact spaces, follows as well. The above facts cannot be extended to noncommutative von Neumann algebras or general Schwartz spaces. Archive classification: General Topology; Functional Analysis Mathematics Subject Classification: 43A35; 46A99; 22A10 Remarks: 11 pages The source file(s), unitfreejunio2006.tex: 39726 bytes, is(are) stored in gzipped form as 0607193.gz with size 13kb. The corresponding postcript file has gzipped size 62kb. Submitted from: jgalindo(a)mat.uji.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GN/0607193 or http://arXiv.org/abs/math.GN/0607193 or by email in unzipped form by transmitting an empty message with subject line uget 0607193 or in gzipped form by using subject line get 0607193 to: math(a)arXiv.org.

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Abstract of a paper by Michael Cwikel and Svante Janson
by Dale Alspach 23 Jun '06

23 Jun '06

This is an announcement for the paper "Complex interpolation of compact operators mapping into the couple (FL^{\infty},FL_{1}^{\infty})" by Michael Cwikel and Svante Janson. Abstract: If (A_0,A_1) and (B_0,B_1) are Banach couples and a linear operator T from A_0 + A_1 to B_0 + B_1 maps A_0 compactly into B_0 and maps A_1 boundedly into B_1, does T necessarily also map [A_0,A_1]_s compactly into [B_0,B_1]_s for s in (0,1)? After 42 years this question is still not answered, not even in the case where T is also compact from A_1 to B_1. But affirmative answers are known for many special choices of (A_0,A_1) and (B_0,B_1). Furthermore it is known that it would suffice to resolve this question in the special case where (B_0,B_1) is the special couple (l^\infty(FL^\infty), l^\infty(FL^\infty_1)). Here FL^\infty is the space of all sequences which are Fourier coefficients of bounded functions, FL^\infty_1 is the weighted space of all sequences (a_n) such that (e^n a_n) is in FL^\infty, and thus B_0 and B_1 are the spaces of bounded sequences of elements in these spaces (i.e., they are spaces of doubly indexed sequences). We provide an affirmative answer to this question in the related but simpler case where (B_0,B_1) is the special couple (FL^\infty,FL^\infty_1). Archive classification: Functional Analysis Mathematics Subject Classification: 46B70 Remarks: 21 pages The source file(s), sj192.tex: 81719 bytes, is(are) stored in gzipped form as 0606551.gz with size 22kb. The corresponding postcript file has gzipped size 106kb. Submitted from: svante.janson(a)math.uu.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606551 or http://arXiv.org/abs/math.FA/0606551 or by email in unzipped form by transmitting an empty message with subject line uget 0606551 or in gzipped form by using subject line get 0606551 to: math(a)arXiv.org.

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Banach space theory - Last announcement
by Félix Cabello Sánchez 22 Jun '06

22 Jun '06

Dear colleague, this is the last announcement of the Satellite conference of the world congress ICM2006: Banach space theory: classical topics and new directions http://www.banachspaces.com The conference aim is to contemplate the topic of Banach spaces from an open and broader point of view; so, in addition to classical Banach space theory, related topics of active research have been included. There will be a special session on Polynomials on Banach spaces organized by R. Aron, D. García and M. Maestre. The main lines of the conference can thus be described as: ·Structure and geometry of infinite dimensional Banach and quasi-Banach spaces ·Infinite dimensional topology ·Asymptotic geometric analysis ·Categorical and homological methods ·Applications of descriptive set theory ·Polynomials on Banach spaces The list of main speakers includes so far: S. Argyros, National Technical University, Athens, Greece J. Bastero, Universidad de Zaragoza, Zaragoza, Spain F. Bombal, Universidad Complutense, Madrid, Spain G. Godefroy, Université Paris 6, Paris, France N.J. Kalton, University of Missouri, Columbia (Missouri), USA J. Lindenstrauss, The Hebrew University of Jerusalem, Jerusalem, Israel V. Milman, University of Tel Aviv, Tel Aviv, Israel A. Naor, Microsoft Research, Redmond (Washington), USA J. Orihuela, Universidad de Murcia, Murcia, Spain A. Rodríguez-Palacios, Universidad de Granada, Granada, Spain S. Szarek, Case Western Reserve University, Cleveland (Ohio), USA E. Odell, University of Texas, Austin (Texas), USA M. Valdivia, Universidad de Valencia, Valencia, Spain General information about the conference Place. The conference will take place in Cáceres, in the Complejo Cultural San Francisco, from 4 to 8 September, 2006. Registration. The ordinary registration fee is 100 EUR. For students, there is a reduced fee of 50 EUR. There is also a combined offer that includes catering and accommodation. See Combined offer to read about it. Catering. You are offered the possibility of getting a ticket that allows you to have breakfast and lunch (not dinner) from 4 to 8 September. Price is 80 EUR. There is also a combined offer that includes registration fee and accommodation. See Combined offer to read about it. Accommodation. There is the possibility of housing at the Residence Diego Muñoz Torrero, placed in front of the site of the conference. Price is 30 EUR per day and person in double room. There is also a combined offer that includes registration fee and catering. See Combined offer to read about it. Of course, you can choose to look for your own accommodation. A list of some hotels appears in the conference web-site. Combined offer. You can choose a combined offer registration that includes: registration fee, accommodation at the Residence Diego Muñoz Torrero, and catering (breakfast and lunch, not dinner) during the conference, for a total of 300 EUR. Invited lectures. It is intended that in the mornings there will take place the invited lectures by the main speakers. Contributed talks. In the evenings, there will be sessions of contributed talks of 15-30 min. People willing to deliver a talk are encouraged to send an abstract using the proper form at the web site. Deadline for submission of abstracts is July 15, 2006. Thematic sessions. There is the possibility to group contributed talks in thematic sessions. People interested in organizing such sessions should send a proposal to the contact address of the organization. Proceedings. The proceedings of the conference shall be published in the journal Extracta Mathematicae. The deadline for submissin of abstracts is 21 December 2006. History of Banach Space Conferences. Since 1996, the Department of Mathematics of the University of Extremadura organizes, at even years, a Banach Spaces conferece in either Badajoz or Cáceres. The proceedings of Conferences I-IV have appeared in Extracta Mathematicae and can be found at http://www.unex.es/extracta/extracta.html. The proceedings of the V Conference will be published by the Cambridge University Press as a volume in the Lecture Notes Series of the London Mathematical Society. All the information about the V Conference (Cáceres, 2004) and its proceedings can be found at http://www.banachspaces.com/banach04 Scientific Committee W.B. Johnson, Texas A&M University, College Station (Texas), USA J. Lindenstrauss, The Hebrew University of Jerusalem, Jerusalem, Israel B. Maurey, Université Paris 7, Paris, France A. Pajor, Université de Marne-la-Vallée, Marne-la-Vallée, France A. Pelczynski, Polish Academy of Sciences, Warsawa, Poland D. Preiss, University College London, London, UK N. Tomczak-Jaegermann, University of Alberta, Edmonton (Alberta), Canada J.M.F. Castillo, Universidad de Extremadura, Badajoz, Spain -- Banach space theory: classical topics & new directions

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