Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Antonio Aviles, Antonio J. Guirao, Jose Rodriguez
by alspach＠math.okstate.edu 07 Jan '13

07 Jan '13

This is an announcement for the paper "On the Bishop-Phelps-Bollobas property for numerical radius in C(K)-spaces" by Antonio Aviles, Antonio J. Guirao, Jose Rodriguez. Abstract: We study the Bishop-Phelps-Bollobas property for numerical radius within the framework of C(K) spaces. We present several sufficient conditions on a compact space K ensuring that C(K) has the Bishop-Phelps-Bollobas property for numerical radius. In particular, we show that C(K) has such property whenever K is metrizable. Archive classification: math.FA Mathematics Subject Classification: 46B20, 47A12, 54E45 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.6761 or http://arXiv.org/abs/1212.6761

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Abstract of a paper by Ryan Causey
by alspach＠math.okstate.edu 07 Jan '13

07 Jan '13

This is an announcement for the paper "Estimation of the Szlenk index of Banach spaces via Schreier spaces" by Ryan Causey. Abstract: For each ordinal $\alpha<\omega_1$, we prove the existence of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of spaces with Szlenk index not exceeding $\omega^\alpha$. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B28 Submitted from: rcausey(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.5576 or http://arXiv.org/abs/1212.5576

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Bob Phelps
by Dale Alspach 06 Jan '13

06 Jan '13

I just learned from Isaac Namioka that Bob Phelps died on January 4th. Dale Alspach

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Lindenstrauss' memorial conference
by Dale Alspach 31 Dec '12

31 Dec '12

---------- Forwarded message ---------- From: "Tomek Szankowski" <tomek.szankowski(a)mail.huji.ac.il> The Hebrew University is organizing a memorial conference for Joram Lindenstrauss. The conference, titled " Banach Spaces: Geometry and Analysis " will be held in Jerusalem , May 26-31, 2013. Participation is open to all. The site of the conference (containing the main speakers' list and the registration form) is http://www.as.huji.ac.il/content/banach-spaces-geometry-and-analysis-0 Tomek Szankowski

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Sad News
by Dale Alspach 20 Dec '12

20 Dec '12

Today, December 20 in the morning, after prolonged illness, died Aleksander Pelczynski, one of the founding fathers of modern Banach space theory. P. Wojtaszczyk Interdyscyplinarne Centrum Modelowania Matematycznego i Komputerowego Uniwersytet Warszawski, Ul. Prosta 69 second floor 00-838 Warszawa

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Abstract of a paper by Jean Bourgain
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "On the Hardy-Littlewood maximal function for the cube" by Jean Bourgain. Abstract: It is shown that the Hardy-Littlewood maximal function associated to the cube in $\mathbb R^n$ obeys dimensional free bounds in $L^p$ fir $p>1$. Earlier work only covered the range $p>\frac 32$. Archive classification: math.FA Mathematics Subject Classification: 42B25 Remarks: 20 pages Submitted from: bourgain(a)ias.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.2661 or http://arXiv.org/abs/1212.2661

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Abstract of a paper by Yoav Kallus and Fedor Nazarov
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "In which dimensions is the ball relatively worst packing?" by Yoav Kallus and Fedor Nazarov. Abstract: It was conjectured by Ulam that the ball has the lowest optimal lattice packing density out of all convex, origin-symmetric three-dimensional solids. We affirm a local version of this conjecture: the ball has a lower optimal lattice packing than any body of sufficiently small asphericity in three dimensions. We also show that in dimensions 4, 5, 6, 7, 8, and 24 there are bodies of arbitrarily small asphericity that pack worse than balls. Archive classification: math.MG cond-mat.soft math.FA Remarks: 15 pages, 1 figure Submitted from: ykallus(a)princeton.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.2551 or http://arXiv.org/abs/1212.2551

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Abstract of a paper by Vladimir P. Fonf, Michael Levin and Clemente Zanco
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "Covering $L^p$ spaces by balls" by Vladimir P. Fonf, Michael Levin and Clemente Zanco. Abstract: We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls. Archive classification: math.FA math.GN Mathematics Subject Classification: Primary 46B20, Secondary 54D20 Submitted from: mlevine(a)cs.bgu.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.2817 or http://arXiv.org/abs/1212.2817

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Abstract of a paper by Jaegil Kim
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "Minimal volume product near Hanner polytopes" by Jaegil Kim. Abstract: Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in a fixed dimension. It is known that every Hanner polytope has the same volume product as the cube or the cross-polytope. In this paper we prove that every Hanner polytope is a strict local minimizer for the volume product in the class of symmetric convex bodies endowed with the Banach-Mazur distance. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20, 52A40, 52B11 Submitted from: jkim(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.2544 or http://arXiv.org/abs/1212.2544

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Abstract of a paper by Vincent Lafforgue and Assaf Naor
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "Vertical versus horizontal Poincar\'e inequalities on the Heisenberg group" by Vincent Lafforgue and Assaf Naor. Abstract: Let $\H= \left\langle a,b\,|\, a[a,b]=[a,b]a\ \wedge\ b[a,b]=[a,b]b\right\rangle$ be the discrete Heisenberg group, equipped with the left-invariant word metric $d_W(\cdot,\cdot)$ associated to the generating set $\{a,b,a^{-1},b^{-1}\}$. Letting $B_n= \{x\in \H:\ d_W(x,e_\H)\le n\}$ denote the corresponding closed ball of radius $n\in \N$, and writing $c=[a,b]=aba^{-1}b^{-1}$, we prove that if $(X,\|\cdot\|_X)$ is a Banach space whose modulus of uniform convexity has power type $q\in [2,\infty)$ then there exists $K\in (0,\infty)$ such that every $f:\H\to X$ satisfies \begin{multline*} \sum_{k=1}^{n^2}\sum_{x\in B_n}\frac{ \|f(xc^k)-f(x)\|_X^q}{k^{1+q/2}}\\\le K\sum_{x\in B_{21n}} \Big(\|f(xa)-f(x)\|^q_X+\|f(xb)-f(x)\|^q_X\Big). \end{multline*} It follows that for every $n\in \N$ the bi-Lipschitz distortion of every $f:B_n\to X$ is at least a constant multiple of $(\log n)^{1/q}$, an asymptotically optimal estimate as $n\to\infty$. Archive classification: math.MG math.FA math.GR Submitted from: naor(a)cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.2107 or http://arXiv.org/abs/1212.2107

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