March 2014 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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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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Abstract of a paper by Dustin G. Mixon
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Explicit matrices with the Restricted Isometry Property: Breaking the square-root bottleneck" by Dustin G. Mixon. Abstract: Matrices with the restricted isometry property (RIP) are of particular interest in compressed sensing. To date, the best known RIP matrices are constructed using random processes, while explicit constructions are notorious for performing at the "square-root bottleneck," i.e., they only accept sparsity levels on the order of the square root of the number of measurements. The only known explicit matrix which surpasses this bottleneck was constructed by Bourgain, Dilworth, Ford, Konyagin and Kutzarova. This chapter provides three contributions to further the groundbreaking work of Bourgain et al.: (i) we develop an intuition for their matrix construction and underlying proof techniques; (ii) we prove a generalized version of their main result; and (iii) we apply this more general result to maximize the extent to which their matrix construction surpasses the square-root bottleneck. Archive classification: math.FA cs.IT math.CO math.IT Remarks: Book chapter, submitted to Compressed Sensing and its Applications Submitted from: dustin.mixon(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3427 or http://arXiv.org/abs/1403.3427

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Abstract of a paper by A. Elbour, N. Machrafi, and M. Moussa
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "Weak compactness of almost limited operators" by A. Elbour, N. Machrafi, and M. Moussa. Abstract: The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma $-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F $ is weakly compact if and only if $E$ is reflexive or the norm of $F$ is order continuous. Also, we show that if $E$ is a $\sigma $-Dedekind complete Banach lattice then the square of every positive almost limited operator $ T:E\rightarrow E$ is weakly compact if and only if the norm of $E$ is order continuous. Archive classification: math.FA Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary) Remarks: 5 pages Submitted from: azizelbour(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3348 or http://arXiv.org/abs/1403.3348

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Abstract of a paper by Jan-David Hardtke
by alspach＠math.okstate.edu 30 Mar '14

30 Mar '14

This is an announcement for the paper "WORTH property, Garc\'{i}a-Falset coefficient and Opial property of infinite sums" by Jan-David Hardtke. Abstract: We prove some results concerning the WORTH property and the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. The Opial property/uniform Opial property of infinite $\ell^p$-sums is also studied and some properties analogous to the Opial property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\mu,X)$ are discussed. Archive classification: math.FA Mathematics Subject Classification: 46B20 46E40 Remarks: 22 pages Submitted from: hardtke(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.2647 or http://arXiv.org/abs/1403.2647

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