December 2012 - 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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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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Abstract of a paper by Pierre Youssef
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "A note on column subset selection" by Pierre Youssef. Abstract: Given a matrix U, using a deterministic method, we extract a "large" submatrix of U'(whose columns are obtained by normalizing those of U) and estimate its smallest and largest singular value. We apply this result to the study of contact points of the unit ball with its maximal volume ellipsoid. We consider also the paving problem and give a deterministic algorithm to partition a matrix into almost isometric blocks recovering previous results of Bourgain-Tzafriri and Tropp. Finally, we partially answer a question raised by Naor about finding an algorithm in the spirit of Batson-Spielman-Srivastava's work to extract a "large" square submatrix of "small" norm. Archive classification: math.FA Remarks: 12 pages Submitted from: pierre.youssef(a)univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.0976 or http://arXiv.org/abs/1212.0976

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Abstract of a paper by Jose Bonet, Carmen Fernandez, Antonio Galbis, and Juan M. Ribera
by alspach＠math.okstate.edu 17 Dec '12

17 Dec '12

This is an announcement for the paper "Shrinking and boundedly complete atomic decompositions in Fr\'echet spaces" by Jose Bonet, Carmen Fernandez, Antonio Galbis, and Juan M. Ribera. Abstract: We study atomic decompositions in Fr\'echet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete atomic decompositions on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional atomic decomposition is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete atomic decompositions in function spaces are also presented. Archive classification: math.FA Mathematics Subject Classification: Primary: 46A04, secondary: 42C15 Submitted from: antonio.galbis(a)uv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1212.0969 or http://arXiv.org/abs/1212.0969

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