December 2010 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Mark W. Meckes
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Positive definite metric spaces" by Mark W. Meckes. Abstract: Magnitude is a numerical invariant of finite metric spaces, recently introduced by T.\ Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended to infinite metric spaces in several a priori distinct ways. This paper develops the theory of a class of metric spaces, positive definite metric spaces, for which magnitude is more tractable than in general. In particular, it is shown that all the proposed definitions of magnitude coincide for compact positive definite metric spaces. Some additional results are proved about the behavior of magnitude as a function of such spaces, and a number of examples of positive definite metric spaces are found, including all subsets of $L_p$ for $p\le 2$ and Euclidean spheres equipped with the geodesic distance. Finally, some facts about the magnitude of compact subsets of $\ell_p^n$ for $p \le 2$ are proved, generalizing results of Leinster for $p=1,2$, using properties of these spaces which are somewhat stronger than positive definiteness. Archive classification: math.MG math.FA math.GN Submitted from: mark.meckes(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5863 or http://arXiv.org/abs/1012.5863

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Abstract of a paper by Orest Bucicovschi and Jiri Lebl
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "On the continuity and regularity of convex extensions" by Orest Bucicovschi and Jiri Lebl. Abstract: We study continuity and regularity of convex extensions of functions from a compact set $C$ to its convex hull $K$. We show that if $C$ contains the relative boundary of $K$, and $f$ is a continuous convex function on $C$, then $f$ extends to a continuous convex function on $K$ using the standard convex roof construction. In fact, a necessary and sufficient condition for $f$ to extend from any set to a continuous convex function on the convex hull is that $f$ extends to a continuous convex function on the relative boundary of the convex hull. We give examples showing that the hypotheses in the results are necessary. In particular, if $C$ does not contain the entire relative boundary of $K$, then there may not exist any continuous convex extension of $f$. Finally, when $\partial K$ and $f$ are $C^1$ we give a necessary and sufficient condition for the convex roof construction to be $C^1$ on all of $K$. We also discuss an application of the convex roof construction in quantum computation. Archive classification: math.FA Mathematics Subject Classification: 52A41, 81P68 Remarks: 12 pages, 2 figures Submitted from: jlebl(a)math.ucsd.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5796 or http://arXiv.org/abs/1012.5796

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Abstract of a paper by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Strictly convex norms and topology" by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski. Abstract: We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit equivalent strictly convex norms, and give an internal topological characterisation of those scattered compact spaces $K$, for which the dual Banach space $C(K)^*$ admits an equivalent strictly convex dual norm. We establish some relationships between (*) and other topological concepts, and the position of several well-known examples in this context. For instance, we show that $C(\mathcal{K})^*$ admits an equivalent strictly convex dual norm, where $\mathcal{K}$ is Kunen's compact space. Also, under the continuum hypothesis CH, we give an example of a compact scattered non-Gruenhage space having (*). Archive classification: math.FA math.GN Submitted from: richard.smith(a)ucd.ie The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5595 or http://arXiv.org/abs/1012.5595

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Abstract of a paper by Antonio Aviles
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Radon-Nikodym compact spaces of low weight and Banach spaces" by Antonio Aviles. Abstract: We prove that a continuous image of a Radon-Nikod\'{y}m compact space of weight less than b is Radon-Nikod\'{y}m compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b. Archive classification: math.FA math.GN Mathematics Subject Classification: Primary 46B26, Secondary 46B22, 46B50, 54G99 Citation: Studia Math. 166 (2005), no. 1, 71–82 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5512 or http://arXiv.org/abs/1012.5512

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Abstract of a paper by Antonio Aviles and Christina Brech
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "A Boolean algebra and a Banach space obtained by push-out iteration" by Antonio Aviles and Christina Brech. Abstract: Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen model. We prove a similar result in the category of Banach spaces. Archive classification: math.LO math.CT math.FA Mathematics Subject Classification: 06E05, 03E35, 03G05, 46B26, 54G05, 18A30 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5051 or http://arXiv.org/abs/1012.5051

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Abstract of a paper by Rodrigo Banuelos and Burgess Davis
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Donald Burkholder's work in martingales and analysis" by Rodrigo Banuelos and Burgess Davis. Abstract: Overview of Burkholder's work on martingales and analysis Archive classification: math.PR math.FA Submitted from: banuelos(a)math.purdue.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4849 or http://arXiv.org/abs/1012.4849

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Abstract of a paper by Rodrigo Banuelos
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "The foundational inequalities of D.L. Burkholder and some of their ramifications" by Rodrigo Banuelos. Abstract: This paper present an overview of some of the applications of the martingale transform inequalities of D.L.~Burkholder to $L^p$-bounds for singular integrals concentrating on $L^p$-bounds for the Hilbert, Riesz, Beurling-Ahlfors transforms and other multipliers obtained by projections (conditional expectations) of transformations of stochastic integrals. The aim is to obtain optimal, or near optimal, bounds in these inequalities. Connections to other areas of mathematics where these inequalities and the techniques to prove them have become of considerable interest in recent years, are also discussed. Archive classification: math.PR math.AP math.FA Submitted from: banuelos(a)math.purdue.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4850 or http://arXiv.org/abs/1012.4850

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Abstract of a paper by D. Azagra, R. Fry, and L. Keener
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space" by D. Azagra, R. Fry, and L. Keener. Abstract: Let $X$ be a separable real Hilbert space. We show that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and for every $\varepsilon>0$, there exists a Lipschitz, real analytic function $g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \varepsilon$ and $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\varepsilon$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 7 pages Submitted from: dazagra(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4339 or http://arXiv.org/abs/1012.4339

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Abstract of a paper by Spiros A. Argyros and Giorgos Petsoulas
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "A $c_0$ saturated Banach space with tight structure" by Spiros A. Argyros and Giorgos Petsoulas. Abstract: It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new $c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight structure. The space $\mathfrak{X}_0$ is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure. Everyone is either of type I, namely, contains an isomorph of $\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type II). Furthermore for any analytic decomposition of $\mathfrak{X}_0$ into two subspaces one is of type I and the other is of type II. The operators of $\mathfrak{X}_0$ share common features with those of HI spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B26 Remarks: 24 pages Submitted from: sargyros(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.2758 or http://arXiv.org/abs/1012.2758

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