Banach

banach@mathdept.okstate.edu

2549 discussions

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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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 characterizations of superreflexivity in terms of word groups and finite graphs" by Mikhail Ostrovskii. Abstract: We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist sequences of series-parallel graphs of increasing topological complexity which admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superreflexivity. Archive classification: math.MG math.CO math.FA math.GR Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12, 20F67, 46B07 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4627 or http://arXiv.org/abs/1312.4627

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Informal Analysis Seminar at Kent State University, 1st-2nd March 2014
by Benjamin Jaye 23 Dec '13

23 Dec '13

Dear Colleague, The Department of Mathematics at Kent State University is happy to announce a meeting of the Kent State Informal Analysis Seminar. The Informal Analysis Seminar will be held on March 1-2, 2014. The plenary lecture series will be given by: Svetlana Jitomirskaya (UC Irvine), and Nets Katz (Caltech) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. The conference is supported by the NSF. 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 at www.math.kent.edu/informal. Please feel free to contact us at informal(a)math.kent.edu for any further information. Attached is a poster that you are welcome to forward to any colleagues you think may be interested. Sincerely, The analysis group at Kent State University.

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Abstract of a paper by Elisabeth M. Werner and Turkay Yolcu
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Equality characterization and stability for entropy inequalities" by Elisabeth M. Werner and Turkay Yolcu. Abstract: We characterize the equality case in a recently established entropy inequality. To do so, we show that characterization of equality is equivalent to uniqueness of the solution of a certain Monge Ampere differential equation. We prove the uniqueness of the solution using methods from mass transport, due to Brenier, and Gangbo-McCann. We then give stability versions for this entropy inequality, as well as for a reverse log Sobolev inequality and for the L_p-affine isoperimetric inequalities for both, log concave functions and convex bodies. In the case of convex bodies such stability results have only been known in all dimensions for p=1 and for p > 1 only for 0-symmetric bodies in the plane. Archive classification: math.FA Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4148 or http://arXiv.org/abs/1312.4148

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Abstract of a paper by Paolo Dulio, Richard J. Gardner and Carla Peri
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Characterizing the dual mixed volume via additive functionals" by Paolo Dulio, Richard J. Gardner and Carla Peri. Abstract: Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the dual mixed volume, the fundamental concept in the dual Brunn-Minkowski theory. The characterizations are shown to be best possible in the sense that none of the assumptions can be omitted. The results obtained are in the spirit of a similar characterization of the mixed volume in the classical Brunn-Minkowski theory, obtained recently by Milman and Schneider, but the methods employed are completely different. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 52A20, 52A30, secondary: 52A39, 52A41 Submitted from: Richard.Gardner(a)wwu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4072 or http://arXiv.org/abs/1312.4072

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