Banach

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Third Announcement of BWB 2014
by valentin ferenczi 26 May '14

26 May '14

THIRD ANNOUNCEMENT OF BWB 2014 First Brazilian Workshop in Geometry of Banach Spaces August 25-29, 2014 Maresias, Sao Paulo State, Brazil. This is the third announcement for the First Brazilian Workshop in Geometry of Banach Spaces, organized by the University of Sao Paulo (USP), in the week August 25-29, 2014, at the Beach Hotel Maresias, on the coast of Sao Paulo State, in Maresias. We would like to recall that the ABSTRACT SUBMISSION deadline, MAY 31st, expires in a few days. Deadline for registration is June 30th. Please access the website of the conference: http://www.ime.usp.br/~banach/bwb2014/ Please CHECK the VISA SITUATION related to your travel document, as requirements for visa depend on bilateral relations between the two countries. For example, participants travelling with a US passport will need a visa. Please consult the website for all information and contact us at bwb2014(a)gmail.com if you have any question. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) P. Dodos (U. Athens) G. Godefroy (Paris 6) W. B. Johnson (Texas A&M) P. Hayek (Czech Acad. & Cz. Polytech. U.) P. Koszmider (Polish Acad. Warsaw) C. Rosendal (U. Illinois Chicago) G. Schechtman (Weizmann Inst.) Th. Schlumprecht (Texas A&M) S. Todorcevic (CNRS Paris & U. Toronto) Scientific committee J. M. F. Castillo (U. Extremadura) V. Ferenczi (U. São Paulo, chair) R. Haydon (U. Oxford) W. B. Johnson (Texas A&M) G. Pisier (Paris 6 & Texas A&M) Th. Schlumprecht (Texas A&M) S. Todorcevic (CNRS Paris & U. Toronto) The organizers, F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.

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Message concerning the death of Manuel Valdivia
by Dale Alspach 22 May '14

22 May '14

--------------------------------- Prof. Manuel Valdivia passed away April the 29th, 2014. He was member of the Spanish Academy of Sciences, professor at the Universitat de Valencia (Spain) and the Universidad Politecnica de Valencia (Spain), and Dr. Honoris Causa at various universities. Author of almost 200 research papers and several books in Functional Analysis, he was one of the outstanding mathematicians in Spain. Condolence messages may be sent to manuelvaldivia2014(a)gmail.com Vicente Montesinos

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Abstract of a paper by Grzegorz Plebanek and Damian Sobota
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "Countable tightness in the spaces of regular probability measures" by Grzegorz Plebanek and Damian Sobota. Abstract: We prove that if $K$ is a compact space and the space $P(K\times K)$ of regular probability measures on $K\times K$ has countable tightness in its $weak^*$ topology, then $L_1(\mu)$ is separable for every $\mu\in P(K)$. It has been known that such a result is a consequence of Martin's axiom MA$(\omega_1)$. Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todor\v{c}evi\'c on measures on Rosenthal compacta. Archive classification: math.FA Mathematics Subject Classification: Primary 46E15, 46E27, 54C35 Remarks: 9 pages Submitted from: grzes(a)math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.2527 or http://arXiv.org/abs/1405.2527

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Abstract of a paper by N. Albuquerque, D. Nunez-Alarcon and D. M. Serrano-Rodríguez
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "A subexponential vector-valued Bohnenblust-Hille type inequality" by N. Albuquerque, D. Nunez-Alarcon and D. M. Serrano-Rodríguez. Abstract: Bayart, Pellegrino and Seoane recently proved that the polynomial Bohnenblust--Hille inequality for complex scalars is subexponential. We show that a vector valued polynomial Bohnenblust-Hille inequality on complex Banach lattices is also subexponential for some special cases. Our main result result recovers the best known constants of the classical polynomial inequality provided in \cite{bps}. Archive classification: math.FA Submitted from: ngalbqrq(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.1204 or http://arXiv.org/abs/1405.1204

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Abstract of a paper by Deping Ye
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas" by Deping Ye. Abstract: This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which are dual to the Orlicz $L_{\phi}$ affine and geominimal surface areas for convex bodies (Ye, arXiv:1403.1643). These new affine invariants belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies (Ye, arXiv:1404.6991). Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequality, cyclic inequality, Santal\'{o} style inequality and Alexander-Fenchel type inequality are established. Besides, an Orlicz isoperimetric inequality for the Orlicz $\phi$-surface area and an Orlicz-Urysohn inequality for the Orlicz $\phi$ mean width are given. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A20, 53A15 Submitted from: deping.ye(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0746 or http://arXiv.org/abs/1405.0746

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Abstract of a paper by Sergey Astashkin
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "Disjointly homogeneous rearrangement invariant spaces via interpolation" by Sergey Astashkin. Abstract: A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory, we clarify which rearrangement invariant (r.i.) spaces on [0,1] are p-disjointly homogeneous. In particular, for every 1<p< infty and any increasing concave function f on [0,1], which is not equivalent neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function f. Moreover, in the class of all interpolation r.i. spaces with respect to the Banach couple of Lorentz and Marcinkiewicz spaces with the same fundamental function, dilation indices of which are non-trivial, for every 1<p< infty, there is only a unique p-disjointly homogeneous space. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B03, 46B70 Remarks: 23 pages Submitted from: astash(a)samsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0681 or http://arXiv.org/abs/1405.0681

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Abstract of a paper by Alexander V. Kolesnikov and Emanuel Milman
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "Remarks on the KLS conjecture and Hardy-type inequalities" by Alexander V. Kolesnikov and Emanuel Milman. Abstract: We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue measures on $\partial \Omega$; these may be bounded via the curvature of $\partial \Omega$. A second reduction is obtained to the class of harmonic functions on $\Omega$. We also study the relation between the Poincar\'e constant of a log-concave measure $\mu$ and its associated K. Ball body $K_\mu$. In particular, we obtain a simple proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk. Archive classification: math.SP math.FA Remarks: 18 pages Submitted from: emanuel.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0617 or http://arXiv.org/abs/1405.0617

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Abstract of a paper by Alexander Koldobsky and Artem Zvavitch
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "An isomorphic version of the Busemann-Petty problem for arbitrary measures" by Alexander Koldobsky and Artem Zvavitch. Abstract: We prove the following theorem. Let $\mu$ be a measure on $R^n$ with even continuous density, and let $K,L$ be origin-symmetric convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any central hyperplane H. Then $\mu(K)\le \sqrt{n} \mu(L).$ We also prove this result with better constants for some special classes of measures and bodies. Finally, we prove a version of the hyperplane inequality for convex measures. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20 Submitted from: koldobskiya(a)missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0567 or http://arXiv.org/abs/1405.0567

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Abstract of a paper by Karl-Mikael Perfekt
by alspach＠math.okstate.edu 15 May '14

15 May '14

This is an announcement for the paper "Weak compactness of operators acting on o-O type spaces" by Karl-Mikael Perfekt. Abstract: We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding "little-o" condition. The main result characterizes the weakly compact operators T in terms of a certain norm naturally attached to M, weaker than the M-norm. Further, we develop a method to extract c_0-subsequences from sequences in M_0. Applications are given to the characterizations of the weakly compact composition and Volterra-type integral operators on weighted spaces of analytic functions, BMOA, VMOA, and the Bloch space. Archive classification: math.FA math.CV Remarks: 12 pages Submitted from: karlmikp(a)math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0502 or http://arXiv.org/abs/1405.0502

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Abstract of a paper by Stanislaw Kwapien, Mark Veraar, and Lutz Weis
by alspach＠math.okstate.edu 02 May '14

02 May '14

This is an announcement for the paper "$R$-boundedness versus $\gamma$-boundedness" by Stanislaw Kwapien, Mark Veraar, and Lutz Weis. Abstract: It is well-known that in Banach spaces with finite cotype, the $R$-bounded and $\gamma$-bounded families of operators coincide. If in addition $X$ is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that $R$-boundedness implies $\gamma$-boundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that $R$-boundedness is stable under taking adjoints if and only if the underlying space is $K$-convex. Archive classification: math.FA math.PR Mathematics Subject Classification: 47B99 (Primary) 46B09, 46B07, 47B10 (Secondary) Submitted from: m.c.veraar(a)tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.7328 or http://arXiv.org/abs/1404.7328

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