Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Gustavo Araujo and Daniel Pellegrino
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Spaceability and optimal estimates for summing multilinear operators" by Gustavo Araujo and Daniel Pellegrino. Abstract: We show that given a positive integer $m$, a real number $p\in\left[ 2,\infty\right) $ and $1\leq s<p^{\ast}$ the set of non--multiple $\left( r,s\right) $--summing $m$--linear forms on $\ell_{p}\times\cdots\times\ell_{p}$ is spaceable whenever $r<\frac{2ms}{s+2m-ms}$. This result is optimal since for $r\geq\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\ell _{p}\times\cdots\times\ell_{p}$ are multiple $\left( r,s\right) $--summing. Among other results, we improve some results from \cite{laa} and generalize a result related to cotype (from 2010) due to Botelho, Michels and the second named author. We also prove some new coincidence results for the class of absolutely summing multilinear operators. Archive classification: math.FA Submitted from: pellegrino(a)pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6064 or http://arXiv.org/abs/1403.6064

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Abstract of a paper by Oleg Reinov
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Some thoughts on approximation properties" by Oleg Reinov. Abstract: We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the properties like the $AP_s$ or $AP_{(s,w)}$ for $s\in (0,1],$ which give us the possibility to identify the spaces of $s$-nuclear and $(s,w)$-nuclear operators with the corresponding tensor products (e.g., related to Lorentz sequence spaces). Some applications are given (in particular, we present not difficult proofs of the trace-formulas of Grothendieck-Lidskii type for several ideals of nuclear operators). Archive classification: math.FA Mathematics Subject Classification: 46B28 Spaces of operators, tensor products, approximation Remarks: 17 pages. A talk at "July 22-26 Positivity 2013 Holland, Leiden" Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4746 or http://arXiv.org/abs/1403.4746

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Workshop at Texas A&M
by Bill Johnson 10 Apr '14

10 Apr '14

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2014 The Summer 2014 Workshop in Analysis and Probability at Texas A&M University will be in session from July 1 to 31, 2014. All activities will take place in the Blocker Building. The homepage of the Workshop can be found at http://www.math.tamu.edu/~kerr/workshop The Summer Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held July 25-27. July 21-25 there will be a Concentration Week on "Free Probability", organized by Michael Anshelevich, Ken Dykema, and John Williams. This meeting aims both to introduce younger researchers to this fast-growing field and to showcase the latest results. Topics discussed will include operator algebras, connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The homepage can be found at http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 Also, June 9-13 there will be a Concentration Week on "Groups, Groupoids, and Dynamics" organized by David Kerr and Volodymyr Nekrashevych (note the special dates, which fall outside the scope of the main Workshop period). This meeting aims to provide a forum for understanding and exploring various recent developments in groups and dynamics that revolve around groupoids and equivalence relations. Topics will include topological orbit equivalence, amenability, hyperbolicity, self-similar groups, entropy, and rigidity in measurable group theory. Lectures series will be given by Lewis Bowen and Thierry Giordano. The homepage can be found at http://www.math.tamu.edu/~kerr/concweek14 The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week on "Free Probability" contact Michael Anshelevich <manshel(a)math.tamu.edu>, Ken Dykema <ken.dykema(a)math.tamu.edu>, or John Williams <jwilliams(a)math.tamu.edu> For information about the Concentration Week on "Groups, Groupoids, Dynamics" contact David Kerr <kerr(a)math.tamu.edu> or Volodymyr Nekrashevych <nekrash(a)math.tamu.edu>.

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Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski
by Jose Rodriguez 02 Apr '14

02 Apr '14

Dear colleagues: This is the third 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 Stanimir Troyanski. The deadline for early registration is April 30. Our web page at https://sites.google.com/site/geometryofbanachspaces/ contains detailed information about the conference, including: registration and payment, abstract submission, accommodation and travel. Main speakers who accepted our invitation are: S. Argyros, J. Castillo, S. Dilworth, M. Fabian, V. Fonf, P. Hajek, R. Haydon, F. Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, J. Revalski, T. Schlumprecht, R. Smith, A. Suarez Granero. In addition, participants will have the opportunity to deliver a short talk. 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 C. Angosto, M. C. Listan-Garcia, and F. Rambla-Barreno
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Continuity properties of sequentially asymptotically center-complete spaces" by C. Angosto, M. C. Listan-Garcia, and F. Rambla-Barreno. Abstract: We obtain formulae to calculate the asymptotic center and radius of bounded sequences in ${\cal C}_0(L)$ spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a H\"older-type estimation is given. Archive classification: math.FA Mathematics Subject Classification: 41A50 (Primary) 46E15 (Secondary) Submitted from: fernando.rambla(a)uca.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4646 or http://arXiv.org/abs/1403.4646

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Abstract of a paper by Daniel Carando, Veronica Dimant, Pablo Sevilla-Peris and Roman Villafane
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Diagonal extendible multilinear operators between $\ell_p$-spaces" by Daniel Carando, Veronica Dimant, Pablo Sevilla-Peris and Roman Villafane. Abstract: We study extendibility of diagonal multilinear operators from $\ell_p$ to $\ell_q$ spaces. We determine the values of $p$ and $q$ for which every diagonal $n$-linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on $\ell_p$. Archive classification: math.FA Mathematics Subject Classification: 47H60, 46B45, 46G25 Submitted from: rvillafa(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4577 or http://arXiv.org/abs/1403.4577

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Abstract of a paper by Marek Cuth and Ondrej F.K. Kalenda
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Monotone retractability and retractional skeletons" by Marek Cuth and Ondrej F.K. Kalenda. Abstract: We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a question of R. Rojas-Hern{\'a}ndez and V. V. Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W. Kubi\'s. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C15, 54D30, 46B26 Remarks: 14 pages Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4480 or http://arXiv.org/abs/1403.4480

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Abstract of a paper by F. Baudier, D. Freeman, Th. Schlumprecht and A. Zsak
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "The metric geometry of the Hamming cube and applications" by F. Baudier, D. Freeman, Th. Schlumprecht and A. Zsak. Abstract: The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the $C(K)$-distortion of important classes of separable Banach spaces, where $K$ is a countable compact space in the family $ \{ [0,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot n],\dots,[0,\omega^\omega]\}\ ,$ are obtained. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B85 Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4376 or http://arXiv.org/abs/1403.4376

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Abstract of a paper by S. J. Dilworth, D. Kutzarova, E. Odell, Th. Schlumprecht and A. Zsak
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Renorming spaces with greedy bases" by S. J. Dilworth, D. Kutzarova, E. Odell, Th. Schlumprecht and A. Zsak. Abstract: We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given $\vare>0$, so that the basis becomes $(1+\vare)$-democratic, and hence $(2+\vare)$-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is $(1+\vare)$-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in $L_p[0,1]$, $1<p<\infty$, and in dyadic Hardy space $H_1$, as well as the unit vector basis of Tsirelson space. Archive classification: math.FA Mathematics Subject Classification: 41A65, 41A44, 41A50, 46B03 Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3777 or http://arXiv.org/abs/1403.3777

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Abstract of a paper by Ralf Beckmann and Anton Deitmar
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Two application of nets" by Ralf Beckmann and Anton Deitmar. Abstract: Two applications of nets are given. The first is an extension of the Bochner integral to arbitrary locally convex spaces, leading to an integration theorye of more general vector valued functions then in the classical approach by Gelfand and Pettis. The second application starts with the observation that an operator on a Hilbert space is trace class if and only if the net of ``principal trace minors'' converges. The notion of a ``determinant class operator'' then is defined as one for which the net of determinantal principal minors converges. It is shown that for a normal operator A this condition coincides with 1-A being trace class. Archive classification: math.FA Submitted from: deitmar(a)uni-tuebingen.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3207 or http://arXiv.org/abs/1403.3207

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