Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces" by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy. Abstract: We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neither ``magic guesses'' nor calculations. Archive classification: math.CA math.DG math.FA Remarks: 11 pages Submitted from: dms(a)pdmi.ras.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.6229 or http://arXiv.org/abs/1405.6229

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Abstract of a paper by Will Grilliette
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Matricial Banach spaces" by Will Grilliette. Abstract: This work performs a study of the category of complete matrix-normed spaces, called matricial Banach spaces. Many of the usual constructions of Banach spaces extend in a natural way to matricial Banach spaces, including products, direct sums, and completions. Also, while the minimal matrix-norm on a Banach space is well-known, this work characterizes the maximal matrix-norm on a Banach space from the work of Effros and Ruan as a dual operator space. Moreover, building from the work of Blecher, Ruan, and Sinclair, the Haagerup tensor product is merged with the direct sum to form a Haagerup tensor algebra, which shares the analogous universal property of the Banach tensor algebra from the work of Leptin. Archive classification: math.FA Mathematics Subject Classification: 46M99 Remarks: 19 pages Submitted from: w.b.grilliette(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5951 or http://arXiv.org/abs/1405.5951

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Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Uniqueness of the maximal ideal of operators on the $\ell_p$-sum of $\ell_\infty^n\ (n\in\mathbb{N})$ for $1<p<\infty$" by Tomasz Kania and Niels Jakob Laustsen. Abstract: A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_p}$ and $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_1^n\bigr)_{\ell_p}$ whenever $p\in(1,\infty)$. Archive classification: math.FA Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5715 or http://arXiv.org/abs/1405.5715

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Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Nigel Kalton and the interpolation theory of commutators" by Michael Cwikel, Mario Milman and Richard Rochberg. Abstract: This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many topics in which Nigel made very significant and profound contributions deals with commutators in interpolation theory. It was our great privilege to work with him on one of his many papers about this topic. Our main purpose here is to offer} an introduction to that paper: A unified theory of commutator estimates for a class of interpolation methods. Adv. Math. 169 (2002), no. 2, 241--312. We sketch the theory of interpolation spaces constructed using pseudolattices which was developed in that paper and which enables quite general formulation of commutator theorems. We seek to place the results of that paper in the general context of preceding and subsequent research on this topic, also indicating some applications to other fields of analysis and possible directions for future research. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70, Secondary 42B20, 42B30, 46B42, 42B37, 35J60 Remarks: 16 pages Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5686 or http://arXiv.org/abs/1405.5686

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Abstract of a paper by Eusebio Gardella and Hannes Thiel
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Banach algebras generated by an invertible isometry of an $L^p$-space" by Eusebio Gardella and Hannes Thiel. Abstract: We study and classify Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. We associate to each such isometry a spectral invariant which contains considerably more information than its spectrum as an operator. We show that this invariant describes the isometric isomorphism type of the Banach algebra that the isometry generates together with its inverse. In the case of invertible isometries with full spectrum, these Banach algebras parametrize all completions of the group algebra $\mathbb{C}[\mathbb{Z}]$ corresponding to unital, contractive representations on $L^p$-spaces. The extreme cases are the algebra of $p$-pseudofunctions on $\mathbb{Z}$, and the commutative $C^*$-algebra $C(S^1)$. Moreover, there are uncountably many non-isometrically isomorphic "intermediate" algebras, all of which are shown to be closed under continuous functional calculus. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary: 46J40, 46H35. Secondary: 47L10 Remarks: 43 pages Submitted from: gardella(a)uoregon.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5589 or http://arXiv.org/abs/1405.5589

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Abstract of a paper by S Dutta and D Khurana
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Ordinal indices for complemented subspaces of l_p" by S Dutta and D Khurana. Abstract: We provide complete isomorphic invariance of a class of translation invariant complemented subspaces of L_p constructed by Bourgain, Rosenthal and Schechtman. We compute ordinal L_p-indices for this class. We further show that the isometric index of a tree subspace over a well founded tree is an invariance for the order of the tree. Finally we provide a dichotomy for the subspaces of L_p with small ordinal indices. Archive classification: math.FA Submitted from: divyakhurana11(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4499 or http://arXiv.org/abs/1405.4499

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Abstract of a paper by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Interpolation of nonlinear maps" by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov. Abstract: Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\subseteq X_0$ with norms satisfying $\|x\|_{X_0} \le c\|x\|_{X_1}$ for some $c > 0$. For any $0<\theta <1$, denote by $X_\theta = [X_0, X_1]_\theta$ and $Y_\theta = [Y_0, Y_1]_\theta$ the complex interpolation spaces and by $B(r, X_\theta)$, $0 \le \theta \le 1,$ the open ball of radius $r>0$ in $X_\theta$, centered at zero. Then for any analytic map $\Phi: B(r, X_0) \to Y_0+ Y_1$ such that $\Phi: B(r, X_0)\to Y_0$ and $\Phi: B(c^{-1}r, X_1)\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respectively, the restriction of $\Phi$ to $B(c^{-\theta}r, X_\theta)$, $0 < \theta < 1,$ is shown to be a map with values in $Y_\theta$ which is analytic and bounded by $M_0^{1-\theta} M_1^\theta$. Archive classification: math.FA Submitted from: p.topalov(a)neu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4253 or http://arXiv.org/abs/1405.4253

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Abstract of a paper by A. Jimenez-Vargas
by alspach＠math.okstate.edu 16 Jun '14

16 Jun '14

This is an announcement for the paper "Weakly compact composition operators on spaces of Lipschitz functions" by A. Jimenez-Vargas. Abstract: Let $X$ be a pointed compact metric space. Assuming that $\mathrm{lip}_0(X)$ has the uniform separation property, we prove that every weakly compact composition operator on spaces of Lipschitz functions $\mathrm{Lip}_0(X)$ and $\mathrm{lip}_0(X)$ is compact. Archive classification: math.FA Mathematics Subject Classification: 47B33, 47B07, 26A16 Remarks: 6 pages Submitted from: ajimenez(a)ual.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4267 or http://arXiv.org/abs/1405.4267

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Informal Analysis and Probability Seminar, October 17-19, 2014
by zvavitch＠math.kent.edu 11 Jun '14

11 Jun '14

Dear Colleague, Analysis/Probability group at the University of Michigan, and the Analysis group at Kent State University are happy to announce a meeting of the Informal Analysis and Probability Seminar, which will run at the Department of Mathematics at University of Michigan October 17-19, 2014. The plenary lecture series will be given by: Olivier Guedon (Pairs-Est University and University of Michigan), and Fedor Nazarov (Kent State) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local expenses, and possibly travel expenses, of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. Further information, and an online registration form, can be found online http://dept.math.lsa.umich.edu/conferences/informalAnalysis/. We encourage you to register as soon as possible, but to receive a support and/or help with hotel reservation, please, do register before September 5, 2014. Please feel free to contact us at rudelson(a)umich.edu / romanv(a)umich.edu for any further information. Sincerely, Analysis/Probability group at the University of Michigan, and the Analysis group at Kent State University

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Fall School ''Metric Embeddings: Constructions and Obstructions''
by BAUDIER Florent 02 Jun '14

02 Jun '14

Dear Colleagues, We are looking for PhD students, postdocs or very young researchers that might be interested in being an active participant of the Fall School ''Metric Embeddings: Constructions and Obstructions'', that we will be organizing in Paris, 3-7 November 2014. The scientific committee will select 12 active participants from the pool of applicants. The deadline to apply is June 30, 2014. The description of the school, its organization and the application and selection processes are fully explained on the website of the Fall School. http://www.math.tamu.edu/~florent/fallschool.html The accommodation in Paris of an active participant will be fully taken care off and we should be able to partially (and eventually fully) cover its travel expenses. Feel free to spread the word to whom you think might be interested. Feel free also, to email us for additional information at florent.baudier(a)imj-prg.fr The organizing committee, F. Baudier (Institut de Mathematiques de Jussieu-Paris Rive Gauche and Texas A&M University) G. Godefroy (Institut de Mathematiques de Jussieu-Paris Rive Gauche, CNRS) P. Pansu (Universite Paris-Sud 11) R. Tessera (Universite Paris-Sud 11, CNRS)

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