Banach January 2014

banach@mathdept.okstate.edu

4 participants
21 discussions

Abstract of a paper by Wilson Cuellar-Carrera
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "A Banach space with a countable infinite number of complex structures" by Wilson Cuellar-Carrera. Abstract: We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures. Archive classification: math.FA Submitted from: cuellar(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.1781 or http://arXiv.org/abs/1401.1781

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Abstract of a paper by Fernando Albiac and Jose L. Ansorena
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Non-existence of greedy bases in direct sums of mixed $\ell_{p}$ spaces" by Fernando Albiac and Jose L. Ansorena. Abstract: The fact that finite direct sums of two or more mutually different spaces from the family $\{\ell_{p} : 1\le p<\infty\}\cup c_{0}$ fail to have greedy bases is stated in [Dilworth et al., Greedy bases for Besov spaces, Constr. Approx. 34 (2011), no. 2, 281-296]. However, the concise proof that the authors give of this fundamental result in greedy approximation relies on a fallacious argument, namely the alleged uniqueness of unconditional basis up to permutation of the spaces involved. The main goal of this note is to settle the problem by providing a correct proof. For that we first show that all greedy bases in an $\ell_{p}$ space have fundamental functions of the same order. As a by-product of our work we obtain that {\it every} almost greedy basis of a Banach space with unconditional basis and nontrivial type contains a greedy subbasis. Archive classification: math.FA Mathematics Subject Classification: 41A35, 46B15 46B45, 46T99 Submitted from: joseluis.ansorena(a)unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0693 or http://arXiv.org/abs/1401.0693

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Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski
by Jose Rodriguez 15 Jan '14

15 Jan '14

Dear colleagues: This is the second announcement of the conference Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski which will be held in Albacete (Spain) on June 10-13, 2014, on the occasion of the 70th birthday of Professor Troyanski. Our web page at https://sites.google.com/site/geometryofbanachspaces/ contains detailed information about the conference. Main speakers who accepted our invitation are: S. Argyros, J. Castillo, S. Dilworth, M. Fabian, V. Fonf, G. Godefroy, P. Hajek, R. Haydon, F. Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, T. Schlumprecht, R. Smith, A. Suarez Granero. Registration is OPEN. Participants must pay a fee which will cover conference materials, lunches and coffee breaks during the conference. Details about the payment can be found in our web page. - Deadline for early registration: April 30. - Deadline for late registration: May 31. Participants will have the opportunity to deliver a short talk. The deadline for abstract submission is May 15. Accommodation: the conference web page includes a list of hotels in Albacete offering special rates for the participants. Please do not hesitate in contacting us at geometry.banach.spaces.2014(a)gmail.com if you need further information. Looking forward to meeting you! The organizers, A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez.

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Abstract of a paper by D. Carando, S. Lassalle, and M. Mazzitelli
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "A Lindenstrauss theorem for some classes of multilinear mappings" by D. Carando, S. Lassalle, and M. Mazzitelli. Abstract: Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their norms. We also consider the class of symmetric multilinear mappings. Archive classification: math.FA Remarks: 11 pages Submitted from: mmazzite(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0488 or http://arXiv.org/abs/1401.0488

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Abstract of a paper by Daniel Fresen
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "Explicit Euclidean embeddings in permutation invariant normed spaces" by Daniel Fresen. Abstract: Let $(X,\left\Vert \cdot \right\Vert )$ be a real normed space of dimension $N\in \mathbb{N}$ with a basis $(e_{i})_{1}^{N}$ such that the norm is invariant under coordinate permutations. Assume for simplicity that the basis constant is at most $2$. Consider any $n\in \mathbb{N}$ and $0<\varepsilon <1/4$ such that $n\leq c(\log \varepsilon ^{-1})^{-1}\log N$. We provide an explicit construction of a matrix that generates a $(1+\varepsilon )$ embedding of $\ell _{2}^{n}$ into $X$. Archive classification: math.FA Mathematics Subject Classification: 46B06, 46B07, 52A20, 52A21, 52A23 Remarks: 14 pages Submitted from: daniel.fresen(a)yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0203 or http://arXiv.org/abs/1401.0203

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Abstract of a paper by Sun Kwang Kim, Han Ju Lee and Miguel Martin
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "On the Bishop-Phelps-Bollobas property for numerical radius" by Sun Kwang Kim, Han Ju Lee and Miguel Martin. Abstract: We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-$\nuu$) and find sufficient conditions for Banach spaces ensuring the BPBp-$\nuu$. Among other results, we show that $L_1(\mu)$-spaces have this property for every measure $\mu$. On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-$\nuu$. In particular, this shows that the Radon-Nikod\'{y}m property (even reflexivity) is not enough to get BPBp-$\nuu$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: hanjulee(a)dongguk.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.7698 or http://arXiv.org/abs/1312.7698

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Abstract of a paper by Alexander Koldobsky
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "A hyperplane inequality for measures of unconditional convex bodies" by Alexander Koldobsky. Abstract: We prove an inequality that extends to arbitrary measures the hyperplane inequality for volume of unconditional convex bodies originally observed by Bourgain. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20 Submitted from: koldobskiya(a)missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.7048 or http://arXiv.org/abs/1312.7048

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Abstract of a paper by Mikhail Ostrovskii
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "Metric spaces nonembeddable into Banach spaces with the property and thick families of geodesics" by Mikhail Ostrovskii. Abstract: We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick family of geodesics is not Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikod\'ym property contains a bilipschitz image of a thick family of geodesics. Archive classification: math.MG math.FA Mathematics Subject Classification: Primary 30L05, Secondary: 46B22, 46B85 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.5381 or http://arXiv.org/abs/1312.5381

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Abstract of a paper by Mohammad N. Ivaki
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "The planar Busemann-Petty centroid inequality and its stability" by Mohammad N. Ivaki. Abstract: In [Centro-affine invariants for smooth convex bodies, Int. Math. Res. Notices. doi: 10.1093/imrn/rnr110, 2011] Stancu introduced a family of centro-affine normal flows, $p$-flow, for $1\leq p<\infty.$ Here we investigate the asymptotic behavior of the planar $p$-flow for $p=\infty$, in the class of smooth, origin-symmetric convex bodies. The motivation is the Busemann-Petty centroid inequality. First, we prove that the $\infty$-flow evolves appropriately normalized origin-symmetric solutions to the unit disk in the Hausdorff metric, modulo $SL(2).$ Second, as an application of this weak convergence, we prove the planar Busemann-Petty centroid inequality in the of class convex bodies having the origin of the plane in their interiors. Third, using the $\infty$-flow, we prove a stability version of the planar Busemann-Petty centroid inequality, in the Banach-Mazur distance, in the class of origin-symmetric convex bodies. Fourth, we prove that the convergence in the Hausdorff metric can be improved to convergence in the $\mathcal{C}^{\infty}$ topology. Archive classification: math.DG math.FA Mathematics Subject Classification: Primary 52A40, 53C44, 52A10, Secondary 35K55, 53A15 Remarks: Two preprints unified into one Submitted from: mohammad.ivaki(a)tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4834 or http://arXiv.org/abs/1312.4834

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Abstract of a paper by Diana Ojeda-Aristizabal
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "Finite forms of Gowers' theorem on the oscillation stability of $c_0$" by Diana Ojeda-Aristizabal. Abstract: We give a constructive proof of the finite version of Gowers' $FIN_k$ Theorem and analyse the corresponding upper bounds. The $FIN_k$ Theorem is closely related to the oscillation stability of $c_0$. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was studied well before by V. Milman. We compare the finite $FIN_k$ Theorem with the finite stabilization principle in the case of spaces of the form $\ell_{\infty}^n$, $n\in\mathbb{N}$ and establish a much slower growing upper bound for the finite stabilization principle in this particular case. Archive classification: math.CO math.FA Mathematics Subject Classification: 05D10 Remarks: 18 pages Submitted from: dco34(a)cornell.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4639 or http://arXiv.org/abs/1312.4639

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Banach January 2014