April 2016 - 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 Matthieu Fradelizi, Mathieu Meyer and Vlad Yaskin
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “On the volume of sections of a convex body by cones” by Matthieu Fradelizi, Mathieu Meyer and Vlad Yaskin. Abstract: Let $K$ be a convex body in $R_n$. We prove that in small codimensions, the sections of a convex body through the centroid are quite symmetric with respect to volume. As a consequence of our estimates we give a positive answer to a problem posed by M. Meyer and S. Reisner regarding convex intersection bodies. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.05351

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Abstract of a paper by Lei Li, Edurado Nieto and Antonio M. Peralta.
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “Geometric implications of the $M(r,s)$-properties and the uniform Kadec-Klee property in JB$^*$-triples” by Lei Li, Edurado Nieto and Antonio M. Peralta. Abstract: We explore new implications of the $M(r,s)$and $M^*(r,s)$properties for Banach spaces. We show that a Banach space $X$ satisfying property $M(1,s)$ for some $0<s\leq 1$ admitting a point $x_0$ in its unit sphere at which the relative weak and norm topologies agree, satisfies the generalized Gossez-Lami Dozo property. We establish sufficient conditions, in terms of the $(r,s)$-Lipschitz weak$^*$ Kadec-Klee property on a Banach space $X$ to guarantee that its dual space satisfies the UKK$^*$ property. We determine appropriate conditions to assure that a Banach space X satisfies the $(r,s)$-Lipschitz weak$^*$ Kadec-Klee property. These results are applied to prove that every spin factor satisfies the UKK property, and consequently, the KKP and the UKK properties are equivalent for real and complex JB$^*$-triples. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.04119

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Abstract of a paper by Mohammed Bachir
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “On the Krein-Milman theorem for convex compact metrizable sets” by Mohammed Bachir. Abstract: The Krein-Milman theorem (1940) states that a convex compact subset of a Hausdorff locally convex topological space, is the closed convex hull of its extreme points. We prove in this paper that in the metrizable case, the situation is better: every convex compact metrizable subset of a Hausdorff locally convex topological space, is the closed convex hull of its exposed points. This fails in general for not metrizable compact convex subsets. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.08473

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Abstract of a paper by Ryan M. Causey
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “The Szlenk index of $C(K,X)$” by Ryan M. Causey. Abstract: Given any Banach space X and any w∗-compact subset $K$ of $X^*$, we compute the Szlenk index of the $w^*$ closed, convex hull of $K$ as a function of the Szlenk index of $K$. As a consequence, for any compact, Hausdorff topological space $K$ and any Banach space $X$, we compute the the Szlenk index of $C(K, X)$ as a function of the Szlenk index of $X$ and the Cantor-Bendixson index of $K$. Also as an application, we compute the Szlenk index of any injective tensor product in terms of $S_z(X)$ and $S_z(Y)$. As another application, we give a complete characterization of those ordinals which occur as the Szlenk index of a Banach space, as well as those ordinals which occur as the Bourgain $\ell_1$ or $c_0$ index of a Banach space. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.07875

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Abstract of a paper by Emanuele Casini, Enrico Miglierina and Lukasz Piasecki
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “Weak$^*$ Fixed Point Property and Polyhedrality in Lindenstrauss Spaces” by Emanuele Casini, Enrico Miglierina and Lukasz Piasecki. Abstract: The main aim of this paper is to study the $w^*$-fixed point property for nonexpansive mappings in the duals of separable Lindestrauss spaces by means of suitable geometrical properties of the dual ball. First we show that a property concerning the behaviour of a class of $w^*$-closed subsets of the dual sphere is equivalent to the $w^*$-fixed point property. Then, the main result of our paper shows an equivalence between another, stronger geometrical property of the dual ball and the stable $w^*$-fixed point property. The last geometrical notion was introduced by Fonf and Vesel$\'{y}$ in 2004 as a strengthening of the notion of polyhedrality. In the last section we show that also the first geometrical assumption that we have introduced can be seen as a polyhedral concept for the predual space. Finally, we prove several relationships between various polyhedrality notions in the framework of Lindenstrauss spaces and we provide some examples showing that none of the considered implications can be reverted. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.07587

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Abstract of a paper by Pavlos Motakis and Thomas Schlumprecht
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “A metric interpretation of reflexivity for Banach spaces” by Pavlos Motakis and Thomas Schlumprecht. Abstract: We define two metrics $d_{1, \alpha}$ and $d_{\infty, \alpha}$ on each Schreier family $S_{\alpha}, \alpha<\omega_1$, with which we prove the following metric characterization of reflexivity of a Banach space $X$: $X$ is reflexive if and only if there is an $\alpha<\omega_1$, so that there is no mapping $\Phi: S_{\alpha}\rightarrow X$ for which $$cd_{\infty, \alpha}(A, B)\leq \|\Phi(A)-\Phi(B)\|\leq Cd_{1, \alpha}(A, B)$$ for all $A, B\in S_{\alpha}$. Secondly, we prove for separable and reflexive Banach spaces $X$, and certain countable ordinals $\alpha$ that max$(S_z(X), Sz(X^*))\leq\alpha$ if and only if $S_{\alpha}d_{1,\alpha}$ does not bi-Lipschitzly embed into $X$. Here $S_z(Y)$ denotes the Szlenk index of a Banach space $Y$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.07271

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Abstract of a paper by Rainis Haller, Katrlin Pirk and Mart Poldvere
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “Diametral strong diameter two property of Banach spaces is stable under direct sums with $1$-norm” by Rainis Haller, Katrlin Pirk and Mart Poldvere. Abstract: We prove that the diametral strong diameter $2$ property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under $1$-sums, i.e., the direct sum of two spaces with the diametral strong diameter $2$ property equipped with the $1$-norm has again this property. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08082

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Abstract of a paper by Pablo M. Berna and Oscar Blasco
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “Characterization of greedy bases in Banach spaces” by Pablo M. Berna and Oscar Blasco. Abstract: We shall present a new characterization of greedy bases and $1$-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.07260

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Abstract of a paper by Tomasz kiwerski and Pawel Kilwicz
by Bentuo Zheng (bzheng) 30 Apr '16

30 Apr '16

This is an announcement for the paper “Isomorphic copies of $l^\infty$ in Cesàro-Orlicz function spaces” by Tomasz kiwerski and Pawel Kilwicz. Abstract: We characterize Ces$\`$aro-Orlicz function spaces $C_{es_{\phi}}$ containing isomorphic copy of $\ell_{\infty}$. We also describe the subspaces $C_{es_{\phi}}$ of all order continuous elements of $C_{es_{\phi}}$. Finally, we study the monotonicity structure of the spaces $C_{es_{\phi}}$ and $(C_{es_{\phi}})_a$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.07257

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