Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Despoina Zisimopoulou
by alspach＠math.okstate.edu 10 Mar '14

10 Mar '14

This is an announcement for the paper "Bourgain-Delbaen $\mathcal{L}^{\infty}$-sums of Banach spaces" by Despoina Zisimopoulou. Abstract: Motivated by a problem stated by S.A.Argyros and Th. Raikoftsalis, we introduce a new class of Banach spaces. Namely, for a sequence of separable Banach spaces $(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$, we define the Bourgain Delbaen $\mathcal{L}^{\infty}$-sum of the sequence $(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$ which is a Banach space $\mathcal{Z}$ constructed with the Bourgain-Delbaen method. In particular, for every $1\leq p<\infty$, taking $X_n=\ell_p$ for every $n\in\mathbb{N}$ the aforementioned space $\mathcal{Z}_p$ is strictly quasi prime and admits $\ell_p$ as a complemented subspace. We study the operators acting on $\mathcal{Z}_p$ and we prove that for every $n\in\mathbb{N}$, the space $\mathcal{Z}^n_p=\sum_{i=1}^n\oplus \mathcal{Z}_p$ admits exactly $n+1$, pairwise not isomorphic, complemented subspaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B25, 46B28 Remarks: 29 pages, no figures Submitted from: dzisimopoulou(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.6564 or http://arXiv.org/abs/1402.6564

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Abstract of a paper by Vladimir P. Fonf and Clemente Zanco
by alspach＠math.okstate.edu 10 Mar '14

10 Mar '14

This is an announcement for the paper "Almost overcomplete and almost overtotal sequences in Banach spaces" by Vladimir P. Fonf and Clemente Zanco. Abstract: The new concepts are introduced of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively norm-compact and we obtain several applications of this fact. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B50, 46B45 Submitted from: clemente.zanco(a)unimi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.6247 or http://arXiv.org/abs/1402.6247

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Piotr Mankiewicz
by Dale Alspach 26 Feb '14

26 Feb '14

With a deep regret we have to inform that Piotr Mankiewicz suddenly passed away on February 21, 2014. We lost a good friend and a good mathematician. He will be missed. If you would like to send a few words to his family please send it to his daughter Ania, at annamankiewicz(a)gmail.com Nicole Tomczak-Jaegermann

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Integration, Vector Measures and Related Topics VI - a reminder
by Grzegorz Plebanek 25 Feb '14

25 Feb '14

This is a reminder about the conference THE MEETING: Integration, Vector Measures and Related Topics VI WHEN: June 15 - 21, 2014 WHERE: the Mathematical Research and Conference Center in Bedlewo (near Poznan, Poland), REGISTRATION and more information on the conference webpage: http://www.math.uni.wroc.pl/~drygier/ivmrt2014/ INVITED SPEAKERS: Antonio Aviles (Murcia), Erik J. Balder (Utrecht), Oscar Blasco (Valencia), Guillermo Curbera (Sevilla), Luisa Di Piazza (Palermo), Harold Garth Dales (Lancaster) Joe Diestel (Kent), Marian Fabian (Prague), David H. Fremlin (Colchester), Ondrej Kalenda (Prague), Zbigniew Lipecki (Wrocaw), Jose Rodriguez (Murcia) The organizing committee: M. Balcerzak, M. Cichon, K. Musial, G. Plebanek

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Second Announcement - BWB 2014
by valentin ferenczi 25 Feb '14

25 Feb '14

2nd ANNOUNCEMENT OF BWB 2014 First Brazilian Workshop in Geometry of Banach Spaces August 25-29, 2014 Maresias, São Paulo State, Brazil. This is the 2nd announcement for the First Brazilian Workshop in Geometry of Banach Spaces, organized by the University of São Paulo (USP), in the week August 25-29, 2014. This international conference will take place at the Beach Hotel Maresias, on the coast of São Paulo State, in Maresias. The scientific program will focus on the theory of geometry of Banach spaces, with emphasis on the following directions: linear theory of infinite dimensional spaces and its relations to Ramsey theory, homological theory and set theory; nonlinear theory; and operator theory. Registration and abstract submissions are now open on the website of conference: http://www.ime.usp.br/~banach/bwb2014/ Deadline for registration is June 30th and for abstract submission is April 30th. 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) J. M. F. Castillo (U. Extremadura) P. Dodos (U. Athens) G. Godefroy (Paris 6) R. Haydon (U. Oxford) W. B. Johnson (Texas A&M) P. Koszmider (Polish Acad. Warsaw) G. Pisier (Paris 6 & Texas A&M) C. Rosendal (U. Illinois Chicago) G. Schechtman (Weizmann Inst.) Th. Schlumprecht (Texas A&M) S. Todorcevic (Paris 7 & 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 (Paris 7 & U. Toronto) The organizers, F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.

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Abstract of a paper by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Schuett and E. M. Werner
by alspach＠math.okstate.edu 21 Feb '14

21 Feb '14

This is an announcement for the paper "Functional versions of L_p-affine surface area and entropy" by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Schuett and E. M. Werner. Abstract: In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities. Archive classification: math.FA Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.3250 or http://arXiv.org/abs/1402.3250

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Abstract of a paper by Mikko Kemppainen
by alspach＠math.okstate.edu 21 Feb '14

21 Feb '14

This is an announcement for the paper "On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators" by Mikko Kemppainen. Abstract: In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X). Archive classification: math.FA Mathematics Subject Classification: 42B35 (Primary), 46E40 (Secondary) Remarks: 19 pages Submitted from: mikko.k.kemppainen(a)helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2886 or http://arXiv.org/abs/1402.2886

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Abstract of a paper by Daniel J. Fresen and Richard A. Vitale
by alspach＠math.okstate.edu 21 Feb '14

21 Feb '14

This is an announcement for the paper "Concentration of random polytopes around the expected convex hull" by Daniel J. Fresen and Richard A. Vitale. Abstract: We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a corresponding strong law of large numbers. Archive classification: math.PR math.FA Mathematics Subject Classification: 60D05, 60F99, 52A20, 52A22, 52B11 Remarks: 8 pages Submitted from: daniel.fresen(a)yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2718 or http://arXiv.org/abs/1402.2718

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Abstract of a paper by Joanna Garbulinska - Wegrzyn
by alspach＠math.okstate.edu 21 Feb '14

21 Feb '14

This is an announcement for the paper "An isometrically universal Banach space with a monotone Schauder" by Joanna Garbulinska - Wegrzyn. Abstract: We present an isometric version of the complementably universal Banach space $\mathcal{B}$ with a monotone Schauder basis. The space $\mathcal{B}$ is isomorphic to Pe\l czy\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B04. Secondary: 46M15, 46M40 Remarks: 10 pages Submitted from: jgarbulinska(a)ujk.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2660 or http://arXiv.org/abs/1402.2660

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Abstract of a paper by Quanhua Xu
by alspach＠math.okstate.edu 21 Feb '14

21 Feb '14

This is an announcement for the paper "$H^\infty$ functional calculus and maximal inequalities for semigroups of contractions on vector-valued $L_p$-spaces" by Quanhua Xu. Abstract: Let $\{T_t\}_{t>0}$ be a strongly continuous semigroup of positive contractions on $L_p(X,\mu)$ with $1<p<\infty$. Let $E$ be a UMD Banach lattice of measurable functions on another measure space $(\Omega,\nu)$. For $f\in L_p(X; E)$ define $$\mathcal M(f)(x, \omega)=\sup_{t>0}\frac1t\Big|\int_0^tT_s(f(\cdot,\omega))(x)ds\Big|,\quad (x,\omega)\in X\times\Omega.$$ Then the following maximal ergodic inequality holds $$\big\|\mathcal M(f)\big\|_{L_p(X; E)}\lesssim \big\|f\big\|_{L_p(X; E)},\quad f\in L_p(X; E).$$ If the semigroup $\{T_t\}_{t>0}$ is additionally assumed to be analytic, then $\{T_t\}_{t>0}$ extends to an analytic semigroup on $L_p(X; E)$ and $\mathcal M(f)$ in the above inequality can be replaced by the following sectorial maximal function $$\mathcal T_\theta(f)(x, \omega)=\sup_{|{\rm arg}(z)|<\theta}\big|T_z(f(\cdot,\omega))(x)\big|$$ for some $\theta>0$. Under the latter analyticity assumption and if $E$ is a complex interpolation space between a Hilbert space and a UMD Banach space, then $\{T_t\}_{t>0}$ extends to an analytic semigroup on $L_p(X; E)$ and its negative generator has a bounded $H^\infty(\Sigma_\sigma)$ calculus for some $\sigma<\pi/2$. Archive classification: math.FA Mathematics Subject Classification: Primary: 47A35, 47A60. Secondary: 46B20, 42B25 Submitted from: quanhua.xu(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2344 or http://arXiv.org/abs/1402.2344

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