Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Mark Rudelson and Roman Vershynin
by Dale Alspach 29 Apr '04

29 Apr '04

This is an announcement for the paper "On random intersections of two convex bodies. Appendix to: "Isoperimetry of waists and local versus global asymptotic convex geometries" by R.Vershynin" by Mark Rudelson and Roman Vershynin. Abstract: In the paper "Isoperimetry of waists and local versus global asymptotic convex geometries", it was proved that the existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of randomly rotated K and L is nicely bounded. In this appendix, we achieve a polynomial bound on the diameter of that intersection (in the ratio of the dimensions of the sections). Archive classification: Functional Analysis Mathematics Subject Classification: 52A20, 46B07 The source file(s), localglobal-appendix.tex: 8336 bytes, is(are) stored in gzipped form as 0404502.gz with size 3kb. The corresponding postcript file has gzipped size 24kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404502 or http://arXiv.org/abs/math.FA/0404502 or by email in unzipped form by transmitting an empty message with subject line uget 0404502 or in gzipped form by using subject line get 0404502 to: math(a)arXiv.org.

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Abstract of a paper by Roman Vershynin
by Dale Alspach 29 Apr '04

29 Apr '04

This is an announcement for the paper "Isoperimetry of waists and local versus global asymptotic convex geometries" by Roman Vershynin. Abstract: Existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of random rotations of K and L is nicely bounded. For L = subspace, this main result immediately yields the unexpected phenomenon: "If K has one nicely bounded section, then most sections of K are nicely bounded". This 'existence implies randomness' consequence was proved independently in [Giannopoulos, Milman and Tsolomitis]. The main result represents a new connection between thelocal asymptotic convex geometry (study of sections of K) and the global asymptotic convex geometry (study K as a whole). The method relies on the new 'isoperimetry of waists' on the sphere due to Gromov. Archive classification: Functional Analysis Mathematics Subject Classification: 52A20,46B07 The source file(s), localglobal.tex: 28490 bytes, is(are) stored in gzipped form as 0404500.gz with size 9kb. The corresponding postcript file has gzipped size 52kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404500 or http://arXiv.org/abs/math.FA/0404500 or by email in unzipped form by transmitting an empty message with subject line uget 0404500 or in gzipped form by using subject line get 0404500 to: math(a)arXiv.org.

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Conference in Granada
by Dale Alspach 28 Apr '04

28 Apr '04

Next September, from the 20th to the 24th, the SECOND INTERNATIONAL COURSE OF MATHEMATICAL ANÃLISIS IN ANDALUCÃA will be held in Granada (Spain). These courses are held every two years in an Andalusian city, with the first being in CÃ¡diz, in September 2002. Our aim is to give an extensive overview of new directions and advances in Mathematical Analysis. Therefore the researcher is invited to get into topics seen promising as guidelines for current and future research in this interesting area of Mathematics. Leading researchers in the area will provide us with a large variety of topics and open problems, showing also some tools and techniques that have been helpful in similar situations. In order to accomplish this goal, both seminars and one-hour talks will be offered. While the one-hour talk are intended to provide an overview on a variety of current topics, the seminars will extend over several days and will therefore allow an in-depth discussion of certain specific subjects. Moreover, all participants of the meeting will have the opportunity to present new results of their research in short communications. The invited speakers of this Second Course are the following: ï· Richard M. Aron (Kent State University, USA) ï· Fernando Bombal (Universidad Complutense de Madrid, Spain) ï· JosÃ© Bonet, (Universidad PolitÃ©cnica de Valencia, Spain). ï· Javier Duoandikoetxea (Universidad del PaÃs Vasco, Spain) ï· Miguel de GuzmÃ¡n (Universidad Complutense de Madrid, Spain) (â ) ï· Gilles Godefroy (U. Paris VI , France ) ï· William B. Johnson (Texas A&M University, USA) ï· Nigel J. Kalton, (University of Missouri, USA) Michael Neumann (Mississippi State University, USA) ï· Lawrence Narici (St. Johnâs University, New York, USA) ï· Kristian Seip (Norwegian University of Sciences and Technology, Norway) ï· Manuel Valdivia (Universidad de Valencia, Spain) ï· Joan Verdera (Universidad AutÃ³noma de Barcelona, Spain) ï· Felipe ZÃ³ (Universidad Nacional de San Luis, Argentina) (â ) We are very sorry to announce the death of Professor Miguel de Guzman (1936-2004), on April 14, 2004. Professor Guzman held a Chair in Mathematical Analysis at the Universidad Complutense de Madrid and was a member of the Royal Academy of Sciences. We had looked forward very much to his participation, as a principal speaker at our meeting. His guidance, leadership, and wisdom will be very much missed. The registration fee is 50 euros for students and 100 euros for all others, provided this fee is paid before July 15th. After July 15, 2004, the fee will be 100 euros for students and 120 euros others. A gala dinner is included in this fee. To formalize the registration process, participants need to complete the inscription form and also to pay the inscription fee. The electronic version of the inscription form is available in our web page: http://www.ugr.es/local/amandal where one can register on-line. Finally if you have problems to coming into our web page please contact us. Lodging is arranged by our Technical Secretary (Eurocongres S.A.) We have rooms in Students Residence Halls at 20 euros per single room per night (subsidized fee) and four star hotels at 60.10 per room per night (which is a special price for our University), with breakfast included. Both the Student Residence Halls and affiliated hotels are located within walking distance to the meeting centre (the Faculty of Science of the Universidad de Granada). We would like to advise you that despite the fact that Granada has many hotels, the number of room we can offer you to this special price is very limited. We therefore strongly suggest that you make your reservation as soon as possible, especially since September is still high season in Granada. Student Residence and hotel rooms will be assigned by strict reservation order and, after that, we cannot guarantee these prices. The scientific program will be complemented by some of the typical attractions of Granada and its surroundings (of course, a visit to the Alhambra is included!). These leisure activities will encourage links of friendship that are so important for every professional group. The Organizing Committee invites you to participate in this meeting with the best wishes that you have a happy and fruitful stay here in Granada. Yours sincerely. MÂª Victoria Velasco Collado (Coordinator) Dpto de AnÃ¡lisis MatemÃ¡tico Facultad de Ciencias Universidad de Granada 18071- Granada (Spain) E-mail : amandal(a)ugr.es

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Abstract of a paper by Piotr W. Nowak
by Dale Alspach 23 Apr '04

23 Apr '04

This is an announcement for the paper "Group actions on Banach spaces and a geometric characterization of a-T-menability" by Piotr W. Nowak. Abstract: We prove a geometric characterization of a-T-menability through proper, affine, isometric actions on subspaces of $L_p[0,1]$ for $1<p<2$. This answers a question of A.~Valette. Archive classification: Metric Geometry; Functional Analysis Remarks: 4 pages The source file(s), a-T-menable-2.tex: 13180 bytes, is(are) stored in gzipped form as 0404402.gz with size 5kb. The corresponding postcript file has gzipped size 33kb. Submitted from: pnowak(a)math.tulane.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0404402 or http://arXiv.org/abs/math.MG/0404402 or by email in unzipped form by transmitting an empty message with subject line uget 0404402 or in gzipped form by using subject line get 0404402 to: math(a)arXiv.org.

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Abstract of a paper by T. Suzuki
by Dale Alspach 23 Apr '04

23 Apr '04

This is an announcement for the paper "Common fixed points of commutative semigroups of nonexpansive mappings" by T. Suzuki. Abstract: In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of common fixed points. In our discussion, we may not assume the strict convexity of the Banach space. Archive classification: Functional Analysis Mathematics Subject Classification: 47H20 Remarks: 18 pages The source file(s), suzuki2.tex: 57526 bytes, is(are) stored in gzipped form as 0404428.gz with size 13kb. The corresponding postcript file has gzipped size 77kb. Submitted from: suzuki-t(a)mns.kyutech.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404428 or http://arXiv.org/abs/math.FA/0404428 or by email in unzipped form by transmitting an empty message with subject line uget 0404428 or in gzipped form by using subject line get 0404428 to: math(a)arXiv.org.

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Abstract of a paper by Piotr W. Nowak
by Dale Alspach 23 Apr '04

23 Apr '04

This is an announcement for the paper "Coarse embeddings of metric spaces into Hilbert spaces" by Piotr W. Nowak. Abstract: There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces $L_p(\mu)$, we get their coarse embeddability into a Hilbert space for $0<p<2$. This together with a theorem by Banach and Mazur yields that coarse embeddability into $\ell_2$ and into $L_p(0,1)$ are equivalent when $1 \le p<2$. A theorem by G.Yu and the above allow to extend to $L_p(\mu)$, $0<p<2$, the range of spaces, coarse embedding into which guarantees for a finitely generated group $\Gamma$ %(viewed as a metric space) to satisfy the Novikov Conjecture. Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 46C05; 46T99 Remarks: 8 pages The source file(s), CoarseembeddingsintoBanachspaces.tex: 25381 bytes, is(are) stored in gzipped form as 0404401.gz with size 8kb. The corresponding postcript file has gzipped size 47kb. Submitted from: pnowak(a)math.tulane.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0404401 or http://arXiv.org/abs/math.MG/0404401 or by email in unzipped form by transmitting an empty message with subject line uget 0404401 or in gzipped form by using subject line get 0404401 to: math(a)arXiv.org.

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Abstract of a paper by A. Brudnyi and Yu. Brudnyi
by Dale Alspach 20 Apr '04

20 Apr '04

This is an announcement for the paper "Metric spaces with linear extensions preserving Lipschitz condition" by A. Brudnyi and Yu. Brudnyi. Abstract: We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor controlled by \lambda(M). We prove that \lambda(M) is finite for several important classes of metric spaces. These include metric trees of arbitrary cardinality, groups of polynomial growth, some groups of exponential growth and certain classes of Riemannian manifolds of bounded geometry. On the other hand we construct an example of a Riemann surface M of bounded geometry for which \lambda(M)=\infty. Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 26B35; 54E35; 46B15 Remarks: 71 pages The source file(s), lip.tex: 181271 bytes, is(are) stored in gzipped form as 0404304.gz with size 53kb. The corresponding postcript file has gzipped size 191kb. Submitted from: albru(a)math.ucalgary.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0404304 or http://arXiv.org/abs/math.MG/0404304 or by email in unzipped form by transmitting an empty message with subject line uget 0404304 or in gzipped form by using subject line get 0404304 to: math(a)arXiv.org.

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Abstract of a paper by Cleon S. Barroso
by Dale Alspach 17 Apr '04

17 Apr '04

This is an announcement for the paper "The fixed point property for a class of nonexpansive maps in L\sp\infty(\Omega,\Sigma,\mu)" by Cleon S. Barroso. Abstract: For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained for the space $C(\Omega)$. An illustrative example is given. Archive classification: Functional Analysis Mathematics Subject Classification: 47H10 Remarks: 4 pages The source file(s), Cleonfp.tex: 11461 bytes, is(are) stored in gzipped form as 0404235.gz with size 4kb. The corresponding postcript file has gzipped size 32kb. Submitted from: cleonbar(a)mat.ufc.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404235 or http://arXiv.org/abs/math.FA/0404235 or by email in unzipped form by transmitting an empty message with subject line uget 0404235 or in gzipped form by using subject line get 0404235 to: math(a)arXiv.org.

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Abstract of a paper by Mark Rudelson and Roman Vershynin
by Dale Alspach 12 Apr '04

12 Apr '04

This is an announcement for the paper "Combinatorics of random processes and sections of convex bodies" by Mark Rudelson and Roman Vershynin. Abstract: We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central Limit Theorem if the square root of its combinatorial dimension is integrable. 2. The uniform entropy is equivalent to the combinatorial dimension under minimal regularity. Our method also constructs a nicely bounded coordinate section of a symmetric convex body in R^n. In the operator theory, this essentially proves for all normed spaces the restricted invertibility principle of Bourgain and Tzafriri. Archive classification: Functional Analysis; Probability Theory Mathematics Subject Classification: 46B09, 60G15, 68Q15 Remarks: 49 pages The source file(s), rv-processes.tex: 122610 bytes, is(are) stored in gzipped form as 0404192.gz with size 38kb. The corresponding postcript file has gzipped size 150kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404192 or http://arXiv.org/abs/math.FA/0404192 or by email in unzipped form by transmitting an empty message with subject line uget 0404192 or in gzipped form by using subject line get 0404192 to: math(a)arXiv.org.

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Abstract of a paper by Mark Rudelson and Roman Vershynin
by Dale Alspach 12 Apr '04

12 Apr '04

This is an announcement for the paper "Random processes via the combinatorial dimension: introductory notes" by Mark Rudelson and Roman Vershynin. Abstract: This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web pages. Archive classification: Functional Analysis; Probability Theory Mathematics Subject Classification: 46B09, 60G15, 68Q15 Remarks: 4 pages The source file(s), rv-processes-description.tex: 12005 bytes, is(are) stored in gzipped form as 0404193.gz with size 5kb. The corresponding postcript file has gzipped size 30kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404193 or http://arXiv.org/abs/math.FA/0404193 or by email in unzipped form by transmitting an empty message with subject line uget 0404193 or in gzipped form by using subject line get 0404193 to: math(a)arXiv.org.

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