November 2015 - 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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Informal Analysis Seminar at Kent State, November 14-15.
by Artem Zvavitch 14 Mar '16

14 Mar '16

Dear Colleague, 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, November 14-15, 2015. The plenary lecture series will be given by: Boaz Klartag (Tel Aviv University) and Igor Rivin (University of St. Andrews) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local and 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 before November 6, 2015. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/Novem… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please, register before October 1, 2015. Please feel free to contact us at informal(a)math.kent.edu for any further information. Sincerely, Analysis Group at Kent State University

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Abstract of a paper by Christos Saroglou and Artem Zvavitch
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "Iterations of the projection body operator and a remark on Petty's conjectured projection inequality" by Christos Saroglou and Artem Zvavitch. Abstract: We prove that if a convex body has absolutely continuous surface area measure, whose density is sufficiently close to the constant, then the sequence $\{\Pi^mK\}$ of convex bodies converges to the ball with respect to the Banach-Mazur distance, as $m\rightarrow\infty$. Here, $\Pi$ denotes the projection body operator. Our result allows us to show that the ellipsoid is a local solution to the conjectured inequality of Petty and to improve a related inequality of Lutwak. Archive classification: math.MG math.FA Remarks: 13 pages Submitted from: csaroglo(a)kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.03381 or http://arXiv.org/abs/1511.03381

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Abstract of a paper by Geraldo Botelho and Ewerton R. Torres
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "Constructing hyper-ideals of multilinear operators between Banach" by Geraldo Botelho and Ewerton R. Torres. Abstract: In view of the fact that some classical methods to construct multi-ideals fail in constructing hyper-ideals, in this paper we develop two new methods to construct hyper-ideals of multilinear operators between Banach spaces. These methods generate new classes of multilinear operators and show that some important well studied classes are Banach or p-Banach hyper-ideals. Archive classification: math.FA Submitted from: botelho(a)ufu.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.03097 or http://arXiv.org/abs/1511.03097

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Abstract of a paper by O. Delgado and E.A. Sanchez Perez
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "Optimal domain of $q$-concave operators and vector measure representation of $q$-concave Banach lattices" by O. Delgado and E.A. Sanchez Perez. Abstract: Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years. Archive classification: math.FA Mathematics Subject Classification: 47B38, 46G10, 46E30, 46B42 Submitted from: easancpe(a)mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.02337 or http://arXiv.org/abs/1511.02337

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Abstract of a paper by Jindrich Lechner
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "1-Grothendieck $C(K)$ spaces" by Jindrich Lechner. Abstract: A Banach space is said to be Grothendieck if weak and weak$^*$ convergent sequences in the dual space coincide. This notion has been quantificated by H. Bendov\'{a}. She has proved that $\ell_\infty$ has the quantitative Grothendieck property, namely, it is 1-Grothendieck. Our aim is to show that Banach spaces from a certain wider class are 1-Grothendieck, precisely, $C(K)$ is 1-Grothendieck provided $K$ is a totally disconnected compact space such that its algebra of clopen subsets has the so called Subsequential completeness property. Archive classification: math.FA Submitted from: jindrich.lechner(a)seznam.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.02202 or http://arXiv.org/abs/1511.02202

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Abstract of a paper by Tomasz Kania and Kent E. Morrison
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "The trace as an average over the unit sphere of a normed space with a 1-symmetric basis" by Tomasz Kania and Kent E. Morrison. Abstract: We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$ for $p\neq 2$. Archive classification: math.FA math.CA Mathematics Subject Classification: 15A60, 47A12 Submitted from: kmorriso(a)calpoly.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.02084 or http://arXiv.org/abs/1511.02084

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Abstract of a paper by David Alonso-Gutierrez, Bernardo Gonzalez Merino, Carlos Hugo Jimenez, and Rafael Villa
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "John's ellipsoid and the integral ratio of a log-concave function" by David Alonso-Gutierrez, Bernardo Gonzalez Merino, Carlos Hugo Jimenez, and Rafael Villa. Abstract: We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional a?ne isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality. Archive classification: math.FA Submitted from: bg.merino(a)tum.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.01266 or http://arXiv.org/abs/1511.01266

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Abstract of a paper by Gonzalo Martinez-Cervantes
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "Riemann integrability versus weak continuity" by Gonzalo Martinez-Cervantes. Abstract: In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space $X$ is said to have the weak Lebesgue property if every Riemann integrable function from $[0,1]$ into $X$ is weakly continuous almost everywhere. We prove that the weak Lebesgue property is stable under $\ell_1$-sums and obtain new examples of Banach spaces with and without this property. Furthermore, we characterize Dunford-Pettis operators in terms of Riemann integrability and provide a quantitative result about the size of the set of $\tau$-continuous non Riemann integrable functions, with $\tau$ a locally convex topology weaker than the norm topology. Archive classification: math.FA Mathematics Subject Classification: 46G10, 28B05, 03E10 Submitted from: gonzalo.martinez2(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.08801 or http://arXiv.org/abs/1510.08801

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Abstract of a paper by L. Garcia-Lirola, J. Orihuela, and M. Raja
by alspach＠math.okstate.edu 12 Nov '15

12 Nov '15

This is an announcement for the paper "Compact convex sets that admit a lower semicontinuous strictly convex function" by L. Garcia-Lirola, J. Orihuela, and M. Raja. Abstract: We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak$^*$ topology. In addition, we find exposed points where a strictly convex lower semicontinuous function is continuous. Archive classification: math.FA Mathematics Subject Classification: 46A55 (Primary) 46B03, 54E35 (Secondary) Remarks: 9 pages Submitted from: luiscarlos.garcia(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.07921 or http://arXiv.org/abs/1510.07921

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