Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Eusebio Gardella, Hannes Thiel
by Bentuo Zheng (bzheng) 01 Apr '17

01 Apr '17

This is an announcement for the paper “Extending representations of Banach algebras to their biduals” by Eusebio Gardella<https://arxiv.org/find/math/1/au:+Gardella_E/0/1/0/all/0/1>, Hannes Thiel<https://arxiv.org/find/math/1/au:+Thiel_H/0/1/0/all/0/1>. Abstract: We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\rightarrow X$ are weakly compact. We apply this to study when the essential space of a representation is complemented. This provides a tool to disregard the difference between degenerate and nondegenerate representations on Banach spaces. As an application we show that a $C^*$-algebra $A$ has an isometric representation on an $L^p$ -space, for $p\in [1, \infty)\{2}$, if and only if $A$ is commutative The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.00882

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Abstract of a paper by Samya Kumar Ray
by Bentuo Zheng (bzheng) 01 Apr '17

01 Apr '17

This is an announcement for the paper “On Multivariate Matsaev's Conjecture” by Samya Kumar Ray<https://arxiv.org/find/math/1/au:+Ray_S/0/1/0/all/0/1>. Abstract: We present various multivariate generalizations of the Matsaev's conjecture in different settings, namely on $L^p$-spaces, non-commutative $L^p$-spaces and semigroups. We show that the multivariate Matsaev's conjecture holds true for any commuting tuple of isometries on $L^p$-spaces. We prove a similar result for Schatten-$p$ classes. We also show that any two parameter strongly continuous semigroup of contractions on a Hilbert space satisfies the multivariate Matsaev's conjecture for semigroups. At the end, we discuss some open questions. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.00733

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Abstract of a paper by Sander C. Hille, Tomasz Szarek, Daniel T.H. Worm, Maria Ziemlanska
by Bentuo Zheng (bzheng) 01 Apr '17

01 Apr '17

This is an announcement for the paper “On a Schur-like property for spaces of measures” by Sander C. Hille<https://arxiv.org/find/math/1/au:+Hille_S/0/1/0/all/0/1>, Tomasz Szarek<https://arxiv.org/find/math/1/au:+Szarek_T/0/1/0/all/0/1>, Daniel T.H. Worm<https://arxiv.org/find/math/1/au:+Worm_D/0/1/0/all/0/1>, Maria Ziemlanska<https://arxiv.org/find/math/1/au:+Ziemlanska_M/0/1/0/all/0/1>. Abstract: A Banach space has the Schur property when every weakly convergent sequence converges in norm. We prove a Schur-like property for measures: if a sequence of finite signed Borel measures on a Polish space is such that it is bounded in total variation norm and such that for each bounded Lipschitz function the sequence of integrals of this function with respect to these measures converges, then the sequence converges in dual bounded Lipschitz norm or Fortet-Mourier norm to a measure. Moreover, we prove three consequences of this result: the first is equivalence of concepts of equicontinuity in the theory of Markov operators, the second is the derivation of weak sequential completeness of the space of signed Borel measures on Polish spaces from our main result and the third concerns conditions for the coincidence of weak and norm topologies on sets of measures that are bounded in total variation norm with additional properties. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.00677

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Conference Announcement
by Bentuo Zheng (bzheng) 22 Mar '17

22 Mar '17

Dear colleagues It is our pleasure to announce this year's special edition of the conference "Journées Besançon-Neuchâtel d'analyse fonctionnelle" which will take place in Besançon, France from June 20 to June 23, 2017. Focusing on the interactions between geometric group theory, functional analysis and non-linear geometry of Banach spaces, the aim of the conference is to bring together researchers and students interested in these fields. The following speakers have agreed to give a plenary talk: Gilles Godefroy, Anastasia Khukhro, Tim de Laat, Masato Mimura, Matias Raja, Christian Rosendal (TBC), Mikael de la Salle, Thomas Schlumprecht, Romain Tessera. You can find more detailed information on our web-page: https://trimestres-lmb.univ-fcomte.fr/besancon-neuchatel2017 Looking forward to seeing you, The organizing committee Gilles Lancien Tony Prochazka Alain Valette

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Trimester on "Analysis in Quantum Information Theory” Sep-Dec 2017 at IHP in Paris
by Stanislaw Szarek 03 Mar '17

03 Mar '17

FINAL(?) ANNOUNCEMENT A Trimester on "Analysis in Quantum Information Theory” will be held at the Institut Henri Poincare in Paris, France, from September 4th to December 15th, 2017. The program will focus on mathematical aspects of QIT and, particularly, on links to broadly understood functional analysis (operator algebras/spaces/systems, asymptotic geometric analysis) and to all flavors of probability. As such, it may be of interest to some members of the Banach mailing list, even though the MSRI semester on “Geometric Functional Analysis and Applications” (which will take place over the same period) is arguably a better match. Planned events include a summer school in early September and three workshop/conferences. Courses, seminars, and collaborative research will take place throughout the duration of the trimester. More information about all activities can be found at https://sites.google.com/site/analysisqit2017/ Registration for the program/events and application for financial support is available via http://www.ihp.fr/en/CEB/T3-2017 Please note that in order to apply for financial support you need to register for the program (indicating the tentative dates of attendance) and NOT just for a particular event. For US-based researchers, there is a dedicated NSF grant that can support their participation, see the first of the above URLs for details. Questions? Email one of the organizers (below) or qit2017(a)ihp.fr for registration/administrative issues. Guillaume Aubrun <aubrun(a)math.univ-lyon1.fr> Benoit Collins <collins(a)math.kyoto-u.ac.jp> Ion Nechita <nechita(a)irsamc.ups-tlse.fr> Stanislaw Szarek <szarek(a)case.edu>

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April 7-9, 2017 - Informal Analysis Seminar at Kent State (Second Announcement)
by Artem Zvavitch 02 Mar '17

02 Mar '17

Dear Colleagues, This is a Second announcement for a meeting of the Informal Analysis Seminar, which will be held at the Department of Mathematical Sciences at Kent State University, April 7 - 9, 2017. This time, the theme of this meeting will be differentiation in finite and infinite dimensional spaces. The seminar will feature talks by Daniel Azagra (Universidad Complutense de Madrid), Estibalitz Durand-Cartagena (UNED, Madrid), Piotr Hajlasz (University of Pittsburgh), Jesús Jaramillo (Universidad Complutense de Madrid), Pekka Koskela, (University of Jyväskylä), Manuel Maestre (University of Valencia), Vladimir Peller (Michigan State University), Patrick J. Rabier (University of Pittsburgh), Pilar Rueda (Universidad de Valencia), Nageswari Shanmugalingam (University of Cincinnati). Similar to previous years, the plan of the meeting will be to have THREE expository, introductory talks on Friday afternoon, April 7, which definitely will be accessible to graduate students. The meeting will end by lunchtime on Sunday, April 9. This time the seminar is supported by Elsevier and Kent State University. Funding is available to cover all local (and possibly help with travel) expenses of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/April… We encourage you to register AS SOON AS POSSIBLE, but to receive support for, and/or help with, hotel reservations, please register-preferably-before MONDAY, MARCH 13, 2017. Finally, please feel free to forward this email to any colleagues or students who you think may be interested in attending. Best regards, The Kent State Analysis Group

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April 7-9, 2017 - Informal Analysis Seminar at Kent State
by Artem Zvavitch 07 Feb '17

07 Feb '17

Dear Colleagues, The Analysis group at Kent State University is happy to announce a meeting of the Informal Analysis Seminar, which will be held at the Department of Mathematical Sciences at Kent State University, April 7 - 9, 2017. This time, the theme of this meeting will be differentiation in finite and infinite dimensional spaces. The seminar will feature talks by Daniel Azagra (Universidad Complutense de Madrid), Estibalitz Durand-Cartagena (Universidad Complutense de Madrid), Piotr Hajlasz (University of Pittsburgh), Jesús Jaramillo (Universidad Complutense de Madrid), Manuel Maestre (University of Valenci), Vladimir Peller (Michigan State University), Patrick J. Rabier (University of Pittsburgh), Pilar Rueda (Universidad de Valencia), Nageswari Shanmugalingam (University of Cincinnati). Similar to previous years, the plan of the meeting will be to have two expository, introductory talks on Friday afternoon, April 7, which definitely will be accessible to graduate students. The meeting will end by lunchtime on Sunday, April 9. This time the seminar is supported by Elsevier and Kent State University. Funding is available to cover the local (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. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/April… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please register before March 6st, 2017. Finally, please feel free to forward this email to any colleagues or students who you think may be interested in attending. Best regards, The Kent State Analysis Group

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Abstract of a paper by A.K.Motovilov, A.A.Shkalikov
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators” by A.K.Motovilov<https://arxiv.org/find/math/1/au:+Motovilov_A/0/1/0/all/0/1>, A.A.Shkalikov<https://arxiv.org/find/math/1/au:+Shkalikov_A/0/1/0/all/0/1>. Abstract: Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\cup_{j\inJ}\Delta_j, J\subset\mathbb{Z}$, of segments $\Delta_j=[\alpha_j,\beta_j]\subset\mathbb{R}$ such that $\alpha_{j+1}>\beta_j$ and $$\inf_j(\alpha_{j+1}-beta_j)=d>0$$. If $B$ is a bounded (in general non-self-adjoint) perturbation of $T$ with $\|B\|=:b<d/2$ then the spectrum of the perturbed operator $A=T+B$ lies in the union $\cup_{j\inJ} U_b(\Delta_j)$ of the mutually disjoint closed $b$-neighborhoods $U_b(\Delta_j)$ of the segments $\Delta_j$ in $\mathbb{C}$. Let $Q_j$ be the Riesz projection onto the invariant subspace of $A$ corresponding to the part of the spectrum of $A$ lying in $U_b(\Delta_j)$. Our main result is as follows: The subspaces $\mathcalL}_j=Q_j(\mathcal{H}), j\in J$, form an unconditional basis in the whole space $\mathcal{H}$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.06296

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Abstract of a paper by Nicolas Monod
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Fixed points in convex cones” by Nicolas Monod<https://arxiv.org/find/math/1/au:+Monod_N/0/1/0/all/0/1>. Abstract: We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous actions, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem for Banach spaces. When restricting to cones that are locally compact in the weak topology, we prove that the property holds for all distal actions, thus extending the general Ryll-Nardzewski theorem for all locally convex spaces. Returning to arbitrary actions, the proposed fixed-point property becomes a group property, considerably stronger than amenability. Equivalent formulations are established and a number of closure properties are proved for the class of groups with the fixed-point property for cones. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.05537

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Abstract of a paper by Willian Hans Goes Corrêa
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Type, cotype and twisted sums induced by complex interpolation” by Willian Hans Goes Corrêa<https://arxiv.org/find/math/1/au:+Correa_W/0/1/0/all/0/1>. Abstract: This paper deals with extensions or twisted sums of Banach spaces that come induced by complex interpolation and the relation between the type and cotype of the spaces in the interpolation scale and the nontriviality and singularity of the induced extension. The results are presented in the context of interpolation of families of Banach spaces, and are applied to the study of submodules of Schatten classes. We also obtain nontrivial extensions of spaces without the CAP which also fail the CAP. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.07084

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