May 2013 - 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 Marius Junge and Carlos palazuelos
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Channel capacities via $p$-summing norms" by Marius Junge and Carlos palazuelos. Abstract: In this paper we show how \emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \emph{Shannon's information theory}. Furthermore, in the last years Shannon's theory has been generalized to the quantum setting to let the \emph{quantum information theory} step in. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. In particular these capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. To deal with the quantum case we will use the noncommutative version of $p$-summing maps. More precisely, we prove that the (product state) classical capacity of a quantum channel with restricted assisted entanglement can be expressed as the derivative of a completely $p$-summing norm. Archive classification: math.FA math.OA quant-ph Submitted from: carlospalazuelos(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.1020 or http://arXiv.org/abs/1305.1020

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Abstract of a paper by L.K.Vashisht and Geetika Khattar
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "On $\mathfrak{I}$-reconstruction property" by L.K.Vashisht and Geetika Khattar. Abstract: Reconstruction property in Banach spaces introduced and studied by Casazza and Christensen in [1]. In this paper we introduce reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property. A characterization of reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property in terms of frames in Banach spaces is obtained. Banach frames associated with reconstruction property are discussed. Archive classification: math.FA Mathematics Subject Classification: 42C15, 42C30, 46B15 Submitted from: lalitkvashisht(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.0334 or http://arXiv.org/abs/1305.0334

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Abstract of a paper by Krzysztof Bolibok, Andrzej Wisnicki and Jacek Wosko
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "The minimal displacement and extremal spaces" by Krzysztof Bolibok, Andrzej Wisnicki and Jacek Wosko. Abstract: We show that both separable preduals of $L_{1}$ and non-type I $C^*$-algebras are strictly extremal with respect to the minimal displacement of $k$-Lipschitz mappings acting on the unit ball of a Banach space. In particular, every separable $C(K)$ space is strictly extremal. Archive classification: math.FA Submitted from: awisnic(a)hektor.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.0246 or http://arXiv.org/abs/1305.0246

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Abstract of a paper by Trond Abrahamsen, Vegard Lima, and Olav Nygaard
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Remarks on diameter 2 properties" by Trond Abrahamsen, Vegard Lima, and Olav Nygaard. Abstract: If $X$ is an infinite-dimensional uniform algebra, if $X$ has the Daugavet property or if $X$ is a proper $M$-embedded space, every relatively weakly open subset of the unit ball of the Banach space $X$ is known to have diameter 2, i.e., $X$ has the diameter 2 property. We prove that in these three cases even every finite convex combination of relatively weakly open subsets of the unit ball have diameter 2. Further, we identify new examples of spaces with the diameter 2 property outside the formerly known cases; in particular we observe that forming $\ell_p$-sums of diameter 2 spaces does not ruin diameter 2 structure. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: To appear in Journal of Convex Analysis Submitted from: veli(a)hials.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.7068 or http://arXiv.org/abs/1304.7068

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Abstract of a paper by Konrad J. Swanepoel
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Equilateral sets and a Sch\"utte Theorem for the 4-norm" by Konrad J. Swanepoel. Abstract: A well-known theorem of Sch\"utte (1963) gives a sharp lower bound for the ratio between the maximum distance and minimum distance between n+2 points in n-dimensional Euclidean space. In this brief note we adapt B\'ar\'any's elegant proof of this theorem to the space $\ell_4^n$. This gives a new proof that the largest cardinality of an equilateral set in $\ell_4^n$ is n+1, and gives a constructive bound for an interval $(4-\epsilon_n,4+\epsilon_n)$ of values of p close to 4 for which it is guaranteed that the largest cardinality of an equilateral set in $\ell_p^n$ is n+1. Archive classification: math.MG math.FA Mathematics Subject Classification: Primary 46B20, Secondary 52A21, 52C17 Remarks: 5 pages Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.7033 or http://arXiv.org/abs/1304.7033

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Abstract of a paper by David Preiss and Gareth Speight
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Differentiability of Lipschitz functions in Lebesgue null sets" by David Preiss and Gareth Speight. Abstract: We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of sigma-porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof. Archive classification: math.FA math.CA Mathematics Subject Classification: 46G05, 46T20 Remarks: 33 pages Submitted from: G.Speight(a)Warwick.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.6916 or http://arXiv.org/abs/1304.6916

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Abstract of a paper by K.K. Kampoukos and S.K. Mercourakis
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "On a certain class of $\K$ Banach spaces" by K.K. Kampoukos and S.K. Mercourakis. Abstract: Using a strengthening of the concept of $\K$ set, introduced in this paper, we study a certain subclass of the class of $\K$ Banach spaces; the so called strongly $\K$ Banach spaces. This class of spaces includes subspaces of strongly weakly compactly generated (SWCG) as well as Polish Banach spaces and it is related to strongly weakly $\mathcal{K}$--analytic (SWKA) Banach spaces as the known classes of $\K$ and weakly $\mathcal{K}$--analytic (WKA) Banach spaces are related. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, 54H05, 03E15, Secondary 46B26 Remarks: Topology and its Applications (to appear, 28 pages) Submitted from: smercour(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.6577 or http://arXiv.org/abs/1304.6577

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Abstract of a paper by Daniel Carando, Andreas Defant and Pablo Sevilla-Peris
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Bohr's absolute convergence problem for $\mathcal{H}_p$-Dirichlet in Banach spaces" by Daniel Carando, Andreas Defant and Pablo Sevilla-Peris. Abstract: The Bohr-Bohnenblust-Hille Theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series $\sum_n a_n n^{-s}$ converges uniformly but not absolutely is less than or equal to $1/2$, and this estimate is optimal. Equivalently, the supremum of the absolute convergence abscissas of all Dirichlet series in the Hardy space $\mathcal{H}_\infty$ equals $1/2$. By a surprising fact of Bayart the same result holds true if $\mathcal{H}_\infty$ is replaced by any Hardy space $\mathcal{H}_p$, $1 \le p < \infty$, of Dirichlet series. For Dirichlet series with coefficients in a Banach space $X$ the maximal width of Bohr's strips depend on the geometry of $X$; Defant, Garc\'ia, Maestre and P\'erez-Garc\'ia proved that such maximal width equal $1- 1/\ct(X)$, where $\ct(X)$ denotes the maximal cotype of $X$. Equivalently, the supremum over the absolute convergence abscissas of all Dirichlet series in the vector-valued Hardy space $\mathcal{H}_\infty(X)$ equals $1- 1/\ct(X)$. In this article we show that this result remains true if $\mathcal{H}_\infty(X)$ is replaced by the larger class $\mathcal{H}_p(X)$, $1 \le p < \infty$. Archive classification: math.FA Mathematics Subject Classification: 30B50, 32A05, 46G20 Submitted from: dcarando(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.5377 or http://arXiv.org/abs/1304.5377

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Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Operators on two Banach spaces of continuous functions on locally compact spaces of ordinals" by Tomasz Kania and Niels Jakob Laustsen. Abstract: Denote by $[0,\omega_1)$ the set of countable ordinals, equipped with the order topology, let $L_0$ be the disjoint union of the compact ordinal intervals $[0,\alpha]$ for $\alpha$ countable, and consider the Banach spaces $C_0[0,\omega_1)$ and $C_0(L_0)$ consisting of all scalar-valued, continuous functions which are defined on the locally compact Hausdorff spaces $[0,\omega_1)$ and~$L_0$, respectively, and which vanish eventually. Our main result states that a bounded operator $T$ between any pair of these two Banach spaces fixes a copy of $C_0(L_0)$ if and only if the identity operator on $C_0(L_0)$ factors through $T$, if and only if the Szlenk index of $T$ is uncountable. This implies that the set $\mathscr{S}_{C_0(L_0)}(C_0(L_0))$ of $C_0(L_0)$-strictly singular operators on $C_0(L_0)$ is the unique maximal ideal of the Banach algebra $\mathscr{B}(C_0(L_0))$ of all bounded operators on $C_0(L_0)$, and that $\mathscr{S}_{C_0(L_0)}(C_0[0,\omega_1))$ is the second-largest proper ideal of $\mathscr{B}(C_0[0,\omega_1))$. Moreover, it follows that the Banach space $C_0(L_0)$ is primary and complementably homogeneous. Archive classification: math.FA Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1304.4951 or http://arXiv.org/abs/1304.4951

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