May 2012 - 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 Tao Mei
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "A universal $H_1$-BMO duality theory for semigroups of operators" by Tao Mei. Abstract: Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a $H_1$-BMO duality theory with assumptions only on the semigroup of operators. The H1's are defined by square functions of P. A. Meyer's gradient form. The formulation of the assumptions does not rely on any geometric/metric property of M nor on the kernel of the semigroups of operators. Our main results extend to the noncommutative setting as well, e.g. the case where $L_\infty(M,\mu)$ is replaced by von Neuman algebras with a semifinite trace. We also prove a Carlson embedding theorem for semigroups of operators. Archive classification: math.CA math.FA math.OA Mathematics Subject Classification: 46L51 42B25 46L10 47D06 Remarks: 22 pages Submitted from: mei(a)wayne.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.4424 or http://arXiv.org/abs/1005.4424

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Abstract of a paper by Daniel Pellegrino
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "Sharp coincidences for absolutely summing multilinear operators" by Daniel Pellegrino. Abstract: In this note we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators. We connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar results obtained via the complex interpolation method. Archive classification: math.FA Remarks: This note is part of the author's thesis which is being written for The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.5411 or http://arXiv.org/abs/1204.5411

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Abstract of a paper by Wayne Lawton
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "Spectral envelopes - A preliminary report" by Wayne Lawton. Abstract: The spectral envelope S(F) of a subset of integers is the set of probability measures on the circle group that are weak star limits of squared moduli of trigonometric polynomials with frequencies in F. Fourier transforms of these measures are positive and supported in F - F but the converse generally fails. The characteristic function chiF of F is a binary sequence whose orbit closure gives a symbolic dynamical system O(F). Analytic properties of S(F) are related to dynamical properties of chiF. The Riemann-Lebesque lemma implies that if chiF is minimal, then S(F) is convex and hence S(F) is the closure of the convex hull of its extreme points Se(F). In this paper we (i) review the relationship between these concepts and the special case of the still open 1959 Kadison-Singer problem called Feichtinger's conjecture for exponential functions, (ii) partially characterize of elements in Se(F), for minimal chiF, in terms of ergodic properties of (O(F),lambda) where lambda is a shift invariant probability measure whose existence in ensured by the 1937 Krylov-Bogoyubov theorem, (iii) refine previous numerical studies of the Morse-Thue minimal binary sequence by exploiting a new MATLAB algorithm for computing smallest eigenvalues of 4,000,000 x 4,000,000 matrices, (iv) describe recent results characterizing S(F) for certain Bohr sets F related to quasicrystals, (v) extend these concepts to general discrete groups including those with Kazhdan's T-property, such as SL(n,Z), n > 2, which can be characterized by several equivalent properties such as: any sequence of positive definite functions converging to 1 uniformly on compact subsets converges uniformly. This exotic property may be useful to construct a counterexample to the generalization of Feichtinger's conjecture and hence to provide a no answer to the question of Kadison and Singer whcih they themselves tended to suspect. Archive classification: math.FA Mathematics Subject Classification: 37B10, 42A55, 43A35 Remarks: To appear in Proceedings the Annual Meeting in Mathematics, Bangkok, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.4904 or http://arXiv.org/abs/1204.4904

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Abstract of a paper by Laurent W. Marcoux, Alexey I. Popov, and Heydar Radjavi
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "On almost-invariant subspaces and approximate commutation" by Laurent W. Marcoux, Alexey I. Popov, and Heydar Radjavi. Abstract: A closed subspace of a Banach space $\cX$ is almost-invariant for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T \in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such that $T \cY \subseteq \cY + \cF_T$. In this paper, we study the existence of almost-invariant subspaces of infinite dimension and codimension for various classes of Banach and Hilbert space operators. We also examine the structure of operators which admit a maximal commuting family of almost-invariant subspaces. In particular, we prove that if $T$ is an operator on a separable Hilbert space and if $TP-PT$ has finite rank for all projections $P$ in a given maximal abelian self-adjoint algebra $\fM$ then $T=M+F$ where $M\in\fM$ and $F$ is of finite rank. Archive classification: math.FA math.OA Mathematics Subject Classification: 47A15, 47A46, 47B07, 47L10 Submitted from: a4popov(a)uwaterloo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.4621 or http://arXiv.org/abs/1204.4621

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Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "Quantification of the reciprocal Dunford-Pettis property" by Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We prove in particular that Banach spaces of the form $C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property. Archive classification: math.FA Remarks: 16 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/1204.4308 or http://arXiv.org/abs/1204.4308

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Abstract of a paper by B. de Pagter and A.W. Wickstead
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "Free and projective Banach lattices" by B. de Pagter and A.W. Wickstead. Abstract: We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms and establish some of their fundamental properties. We give much more detailed results about their structure in the case that there are only a finite number of generators and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice $P$ to be projective if whenever $X$ is a Banach lattice, $J$ a closed ideal in $X$, $Q:X\to X/J$ the quotient map, $T:P\to X/J$ a linear lattice homomorphism and $\epsilon>0$ there is a linear lattice homomorphism $\hat{T}:P\to X$ such that (i) $T=Q\circ \hat{T}$ and (ii) $\|\hat{T}\|\le (1+\epsilon)\|T\|$. We establish the connection between projective Banach lattices and free Banach lattices and describe several families of Banach lattices that are projective as well as proving that some are not. Archive classification: math.FA Submitted from: A.Wickstead(a)qub.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.4282 or http://arXiv.org/abs/1204.4282

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Abstract of a paper by Fedor Sukochev and Anna Tomskova
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "(E,F)-multipliers and applications" by Fedor Sukochev and Anna Tomskova. Abstract: For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is the space all of matrices $M$ for which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever $A$ does. We obtain several results asserting continuous embedding of $(E,F)$-multiplier space into the classical $(p,q)$-multiplier space (that is when $E=l_p$, $F=l_q$). Furthermore, we present many examples of symmetric sequence spaces $E$ and $F$ whose projective and injective tensor products are not isomorphic to any subspace of a Banach space with an unconditional basis, extending classical results of S. Kwapie\'{n} and A. Pe{\l}czy\'{n}ski and of G. Bennett for the case when $E=l_p$, $F=l_q$. Archive classification: math.FA Remarks: 16 pages Submitted from: tomskovaanna(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.2623 or http://arXiv.org/abs/1204.2623

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Abstract of a paper by Taras Banakh, Bogdan Bokalo, and Nadiya Kolos
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "On \sigma-convex subsets in spaces of scatteredly continuous functions" by Taras Banakh, Bogdan Bokalo, and Nadiya Kolos. Abstract: We prove that for any topological space $X$ of countable tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$ of scatteredly continuous real-valued functions on $X$ has network weight $nw(\F)\le nw(X)$. This implies that for a metrizable separable space $X$, each compact convex subset in the function space $SC_p(X)$ is metrizable. Another corollary says that two Tychonoff spaces $X,Y$ with countable tightness and topologically isomorphic linear topological spaces $SC_p(X)$ and $SC_p(Y)$ have the same network weight $nw(X)=nw(Y)$. Also we prove that each zero-dimensional separable Rosenthal compact space is homeomorphic to a compact subset of the function space $SC_p(\omega^\omega)$ over the space $\omega^\omega$ of irrationals. Archive classification: math.GN math.FA Mathematics Subject Classification: 46A55, 46E99, 54C35 Remarks: 6 pages Submitted from: tbanakh(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.2438 or http://arXiv.org/abs/1204.2438

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Abstract of a paper by S Dutta and A B Abubaker
by alspach＠math.okstate.edu 08 May '12

08 May '12

This is an announcement for the paper "Generalized 3-circular projections in some Banach spaces" by S Dutta and A B Abubaker. Abstract: Recently in a series of papers it is observed that in many Banach spaces, which include classical spaces $C(\Omega)$ and $L_p$-spaces, $1 \leq p < \infty, p \neq 2$, any generalized bi-circular projection $P$ is given by $P = \frac{I+T}{2}$, where $I$ is the identity operator of the space and $T$ is a reflection, that is, $T$ is a surjective isometry with $T^2 = I$. For surjective isometries of order $n \geq 3$, the corresponding notion of projection is generalized $n$-circular projection as defined in \cite{AD}. In this paper we show that in a Banach space $X$, if generalized bi-circular projections are given by $\frac{I+T}{2}$ where $T$ is a reflection, then any generalized $n$-circular projection $P$, $n \geq 3$, is given by $P = \frac{I+T+T^2+\cdots+T^{n-1}}{n}$ where $T$ is a surjective isometry and $T^n = I$. We prove our results for $n=3$ and for $n > 3$, the proof remains same except for routine modifications. Archive classification: math.FA Mathematics Subject Classification: 47L05, 46B20 Remarks: 8 pages Submitted from: sudipta(a)iitk.ac.in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.2360 or http://arXiv.org/abs/1204.2360

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