Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Ryan M. Causey, Gilles Lancien
by Bentuo Zheng (bzheng) 02 Nov '17

02 Nov '17

This is an announcement for the paper “Prescribed Szlenk index of iterated duals” by Ryan M. Causey<https://arxiv.org/find/math/1/au:+Causey_R/0/1/0/all/0/1>, Gilles Lancien<https://arxiv.org/find/math/1/au:+Lancien_G/0/1/0/all/0/1>. Abstract: In a previous work, the first named author described the set $ \mathbb{P}$ of all values of the Szlenk indices of separable Banach spaces. We complete this result by showing that for any integer $n$ and any ordinal $\alpha$ in $\mathbb{P}$, there exists a separable Banach space $X$ such that the Szlenk of the dual of order $k$ of $X$ is equal to the first infinite ordinal $\omega$ for all $k$ in $\{0,…, n-1\}$ and equal to $\alpha$ for $k=n$. One of the ingredients is to show that the Lindenstrauss space and its dual both have a Szlenk index equal to $\omega$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1710.01638

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Abstract of a paper by Andrew Swift
by Bentuo Zheng (bzheng) 02 Nov '17

02 Nov '17

This is an announcement for the paper “A coding of bundle graphs and their embeddings into Banach spaces” by Andrew Swift<https://arxiv.org/find/math/1/au:+Swift_A/0/1/0/all/0/1>. Abstract: The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial finitely-branching bundle graph. It is likewise shown that asymptotic uniform convexifiability can be characterized within the class of reflexive Banach spaces with an unconditional asymptotic structure by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial $\mathcal{N}_0$-branching bundle graph. The best known distortions are recovered. For the specific case of $L_1$, it is shown that every countably-branching bundle graph bi-Lipschitzly embeds into $L_1$ with distortion no worse than $2$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1710.00877

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Announcement of AOT
by Bentuo Zheng (bzheng) 25 Oct '17

25 Oct '17

This year is the 125th anniversary of Stefan Banach’s birthday, one of the founders of functional analysis. Therefore, Advances in Operator Theory (AOT) starts publication of a special issue on “Trends in Operators on Banach Spaces” We would like to invite you to submit a research paper of high quality to this issue. Its publisher is TMRG, the publisher of http://www.projecteuclid.org/euclid.bjma http://www.projecteuclid.org/euclid.afa There is no publication charge for authors and readers. The journal particularly invites articles related to the following topics but other papers in the scope are welcome. * Special classes of linear operators (unbounded, hypercyclic, Fredholm, Toeplitz, composition, ...) * Banach and operator algebras * Operator spaces * Banach lattices * Banach function spaces * Operator ideals * Geometry of Banach spaces * Complemented and invariant subspaces * Norm inequalities * Bases and Frames * Polynomials and differentiable functions on Banach spaces * Spectral theory of operators * Multivariable operator theory * Factorization of operators * Approximation * Interpolation * Representation * Preserving maps * Positivity * Equations and inequalities involving operators * Semigroups of operators * Differential operators * Integral operators * Fractional powers of linear operators * Functional calculi for linear operators * Nonlinear operators %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Submission should be done via the online submission of AOT at: http://aot-math.org/ The deadline for submission is *** 30 April 2018 *** %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Please let the editor-in-chief (M. S. Moslehian moslehian(a)um.ac.ir<mailto:moslehian@um.ac.ir> and journal(a)aot-math.org<mailto:journal@aot-math.org>) know as soon as you are able to have a contribution to the issue and give him an approximate date for receiving your paper, if possible. Best wishes, Editorial office

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Advances in Operator Theory
by Bentuo Zheng (bzheng) 06 Oct '17

06 Oct '17

Dear colleague, We would like to announce that Volume 3, Issue 1, Winter 2018 of the Advances in Operator Theory (AOT) was published. It is dedicated to the late professor Uffe Haagerup. We would like to invite you to submit a paper of high standard to this journal. Please keep the journal in your mind for your forthcoming paper. http://aot-math.org/ Sincerely yours, M. S. Moslehian Editor-in-chief 1. Complex interpolation and non-commutative integration Klaus Werner Show Article<http://www.aot-math.org/article_42356.html> | Full Text<http://www.aot-math.org/article_42356_71777b147346763bfff24fc7d39d965f.pdf> 2. Semicontinuity and closed faces of C*-algebras Lawrence G. Brown Show Article<http://www.aot-math.org/article_43918.html> | Full Text<http://www.aot-math.org/article_43918_bf8da69fd044f09da9c3e4f4db9277c1.pdf> 3. The closure of ideals of $\ell^1(\Sigma)$ in its enveloping $\mathrm{C}^*$-algebra Marcel de Jeu; Jun Tomiyama Show Article<http://www.aot-math.org/article_44047.html> | Full Text<http://www.aot-math.org/article_44047_f65a8f1062ea283744db5848a9363ba9.pdf> 4. Positive map as difference of two completely positive or super-positive maps Tsuyoshi Ando Show Article<http://www.aot-math.org/article_44116.html> | Full Text<http://www.aot-math.org/article_44116_531ea9ae7786a407c42b2866cb0dd368.pdf> 5. Some natural subspaces and quotient spaces of $L^1$ Gilles Godefroy; Nicolas Lerner Show Article<http://www.aot-math.org/article_44924.html> | Full Text<http://www.aot-math.org/article_44924_ba9c3c5c2f3766d6635df15b74db8914.pdf> 6. Partial isometries: a survey Antonio Peralta; Francisco J Fernandez-Polo Show Article<http://www.aot-math.org/article_45165.html> | Full Text<http://www.aot-math.org/article_45165_94afcb414af03a75e4a512f171c4db10.pdf> 7. Operators with compatible ranges in an algebra generated by two orthogonal projections Ilya M Spitkovsky Show Article<http://www.aot-math.org/article_45166.html> | Full Text<http://www.aot-math.org/article_45166_aed3194d347d41e51b89267a4029d5d6.pdf> 8. Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property Hiroyuki Osaka; Tamotsu Teruya Show Article<http://www.aot-math.org/article_45177.html> | Full Text<http://www.aot-math.org/article_45177_609d8347a1a4c02639504efeafda0dce.pdf> 9. Almost Hadamard matrices with complex entries Teodor Banica; Ion Nechita Show Article<http://www.aot-math.org/article_45905.html> | Full Text<http://www.aot-math.org/article_45905_9d673bba71c41fc688aba52b6f8a1896.pdf> 10. Non-commutative rational functions in strong convergent random variables Sheng Yin Show Article<http://www.aot-math.org/article_46452.html> | Full Text<http://www.aot-math.org/article_46452_614d056f5f7799b607d6277111157ff4.pdf> 11. Fourier multiplier norms of spherical functions on the generalized Lorentz groups Troels Steenstrup Show Article<http://www.aot-math.org/article_47035.html> | Full Text<http://www.aot-math.org/article_47035_188d9dff266918afd8450b07fe22a042.pdf> 12. On a class of Banach algebras associated to harmonic analysis on locally compact groups and semigroups Anthony To-Ming Lau; Hung Le Pham Show Article<http://www.aot-math.org/article_47586.html> | Full Text<http://www.aot-math.org/article_47586_4d00ddd2b10646cbc0d558bf63b4c156.pdf> 13. Uniformly bounded representations and completely bounded multipliers of ${\rm SL}(2,\mathbb{R})$ Francesca Astengo; Michael G. Cowling; Bianca Di Blasio Show Article<http://www.aot-math.org/article_49322.html> | Full Text<http://www.aot-math.org/article_49322_22d66b67cb2a0a25c1f990a92fdf1ff4.pdf> 14. Completely positive contractive maps and partial isometries Berndt Brenken Show Article<http://www.aot-math.org/article_49352.html> | Full Text<http://www.aot-math.org/article_49352_b35db7c10682e142099c3a89ec189db7.pdf> 15. Uffe Haagerup - his life and mathematics Mohammad Sal Moslehian; Erling Stormer; Steen Thorbjoernsen; Carl Winsløw Show Article<http://www.aot-math.org/article_50017.html> | Full Text<http://www.aot-math.org/article_50017_53b4c3d7f46e44ffb517cab097d0a9ae.pdf>

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Abstract of a paper by Menet Quentin
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “Invariant subspaces for non-normable Fréchet spaces” by Menet Quentin<https://arxiv.org/find/math/1/au:+Quentin_M/0/1/0/all/0/1>. Abstract: A Fr\'echet space X satisfies the Hereditary Invariant Subspace (resp. Subset) Property if for every closed infinite-dimensional subspace $M$ in $X$, each continuous operator on $M$ possesses a non-trivial invariant subspace (resp. subset). In this paper, we show that there exist non-normable separable infinite-dimensional Fr\'echet spaces satisfying the Hereditary Invariant Subspace Property but that a large family of non-normable Fr\'echet spaces does not satisfy this property. We also state sufficient conditions for the existence of a continuous operator without non-trivial invariant subset and deduce among other examples that there exists a continuous operator without non-trivial invariant subset on the space of entire functions $\mathbb{H}(C)$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.09933

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Abstract of a paper by J.C. Ferrando, J. Kakol, M. Lopez-Pellicer, W. Sliwa
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “On the separable quotient problem for Banach spaces” by J.C. Ferrando<https://arxiv.org/find/math/1/au:+Ferrando_J/0/1/0/all/0/1>, J. Kakol<https://arxiv.org/find/math/1/au:+Kakol_J/0/1/0/all/0/1>, M. Lopez-Pellicer<https://arxiv.org/find/math/1/au:+Lopez_Pellicer_M/0/1/0/all/0/1>, W. Sliwa<https://arxiv.org/find/math/1/au:+Sliwa_W/0/1/0/all/0/1>. Abstract: While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces $c_0$ and $\ell_p$, for $1\leq p\leq\infty$. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.09646

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Abstract of a paper by Antonio M. Peralta
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “Extending surjective isometries defined on the unit sphere of $\ell_{\infty}(\Gamma)$” by Antonio M. Peralta<https://arxiv.org/find/math/1/au:+Peralta_A/0/1/0/all/0/1>. Abstract: Let $\Gamma$ be an infinite set equipped with the discrete topology. We prove that the space $\ell_{\infty}(\Gamma)$, of all complex-valued bounded functions on $\Gamma$, satisfies the Mazur-Ulam property, that is, every surjective isometry from the unit sphere of $\ell_{\infty}(\Gamma)$ onto the unit sphere of an arbitrary complex Banach space X admits a unique extension to a surjective real linear isometry from $\ell_{\infty}(\Gamma)$ to $X$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.09584

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Abstract of a paper by Zakhar Kabluchko, Joscha Prochno, Christoph Thaele
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “High-dimensional limit theorems for random vectors in $\ell_p^n$-balls” by Zakhar Kabluchko<https://arxiv.org/find/math/1/au:+Kabluchko_Z/0/1/0/all/0/1>, Joscha Prochno<https://arxiv.org/find/math/1/au:+Prochno_J/0/1/0/all/0/1>, Christoph Thaele<https://arxiv.org/find/math/1/au:+Thaele_C/0/1/0/all/0/1>. Abstract: In this paper, we prove a multivariate central limit theorem for $\ell_q$-norms of high-dimensional random vectors that are chosen uniformly at random in an $\ell_p^n$-ball. As a consequence, we provide several applications on the intersections of $\ell_p^n$-balls in the flavor of Schechtman and Schmuckenschl\"ager and obtain a central limit theorem for the length of a projection of an $\ell_p^n$-ball onto a line spanned by a random direction $\theta\in\mathbb{S}_{n-1}$. The latter generalizes results obtained for the cube by Paouris, Pivovarov and Zinn and by Kabluchko, Litvak and Zaporozhets. Moreover, we complement our central limit theorems by providing a complete description of the large deviation behavior, which covers fluctuations far beyond the Gaussian scale. In the regime $1\leq p<q$ this displays in speed and rate function deviations of the $q$-norm on an $\ell_p^n$-ball obtained by Schechtman and Zinn, but we obtain explicit constants. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.09470

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Abstract of a paper by Stephan Fackler, Jochen Glück
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “A Toolkit for Constructing Dilations on Banach Spaces” by Stephan Fackler<https://arxiv.org/find/math/1/au:+Fackler_S/0/1/0/all/0/1>, Jochen Glück<https://arxiv.org/find/math/1/au:+Gluck_J/0/1/0/all/0/1>. Abstract: We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if $X$ is a super-reflexive Banach space and $T$ is contained in the weakly closed convex hull of all invertible isometries on $X$, then $T$ admits a dilation to an invertible isometry on a Banach space $Y$ with the same regularity as $X$. The classical dilation theorems of Sz.-Nagy and Akcoglu-Sucheston are easy consequences of our general theory. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.08547

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Abstract of a paper by Michał Świętek
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “Regular subspaces of a Bourgain-Delbaen space $\mathcal{B}_{mT}$” by Michał Świętek<https://arxiv.org/find/math/1/au:+Swietek_M/0/1/0/all/0/1>. Abstract: The space $\mathcal{B}_{mt}[(m_j)_j, (n_j)_j]$ is a Bourgain-Delbaen space modelled on a mixed Tsirelson space $T[(m_j)_j, (n_j)_j]$ and is a slight modification of $\mathBB{B}_{mt}[(m_j)_j, (n_j)_j]$ a space defined by S. Argyros and R. Haydon. We prove that in every infinite dimensional subspace of $\mathcal{B}_{mt}[(m_j)_j, (n_j)_j]$ there exists a basic sequence equivalent to a sequence of weighted basis averages of increasing length from $T[(m_j)_j, (n_j)_j]$. We remark that the same is true for the original space $\mathBB{B}_{mt}[(m_j)_j, (n_j)_j]$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.06481

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