September 2014 - 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 Kati Ain and Eve Oja
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "On $(p,r)$-null sequences and their relatives" by Kati Ain and Eve Oja. Abstract: Let $1\leq p < \infty$ and $1\leq r \leq p^\ast$, where $p^\ast$ is the conjugate index of $p$. We prove an omnibus theorem, which provides numerous equivalences for a sequence $(x_n)$ in a Banach space $X$ to be a $(p,r)$-null sequence. One of them is that $(x_n)$ is $(p,r)$-null if and only if $(x_n)$ is null and relatively $(p,r)$-compact. This equivalence is known in the ''limit'' case when $r=p^\ast$, the case of the $p$-null sequence and $p$-compactness. Our approach is more direct and easier than those applied for the proof of the latter result. We apply it also to characterize the unconditional and weak versions of $(p,r)$-null sequences. Archive classification: math.FA Submitted from: kati.ain(a)ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.6476 or http://arXiv.org/abs/1409.6476

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Abstract of a paper by Fernanda Botelho and James Jamison
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "Isometries and Hermitian operators on $\mathcal{B}_0(\triangle, E)$" by Fernanda Botelho and James Jamison. Abstract: In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho(a)memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5381 or http://arXiv.org/abs/1409.5381

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Abstract of a paper by Fernanda Botelho
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "Isometries and Hermitian operators on Zygmund spaces" by Fernanda Botelho. Abstract: In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho(a)memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5378 or http://arXiv.org/abs/1409.5378

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Abstract of a paper by Dimosthenis Drivaliaris and Nikos Yannakakis
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "The angle of an operator and range and kernel complementarity" by Dimosthenis Drivaliaris and Nikos Yannakakis. Abstract: We show that if the angle of a bounded linear operator on a Banach space with closed range is less than $\pi$, then its range and kernel are complementary. We also show that in finite dimensions and up to rotations this simple geometric property characterizes operators for which range and kernel are complementary. For operators on a Hilbert space we present a sufficient condition, involving the distance of the boundary of the numerical range from the origin, for the range and the kernel to be complementary. Archive classification: math.FA Mathematics Subject Classification: 47A05, 47A12, 47A10, 47B44, 46B20 Submitted from: d.drivaliaris(a)fme.aegean.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.4195 or http://arXiv.org/abs/1409.4195

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Abstract of a paper by Thomas Schlumprecht and Andras Zsak
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "The algebra of bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals" by Thomas Schlumprecht and Andras Zsak. Abstract: We prove that in the reflexive range $1<p<q<\infty$ the algebra of all bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals. This solves a problem raised by A. Pietsch in his book `Operator ideals'. Archive classification: math.FA Mathematics Subject Classification: 47L20, 46B25 Remarks: 18 pages Submitted from: a.zsak(a)dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.3480 or http://arXiv.org/abs/1409.3480

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Abstract of a paper by Dong Hoon Cho and Yun Sung Choi
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "Bishop-Phelps-Bolloba's theorem on bounded closed convex sets" by Dong Hoon Cho and Yun Sung Choi. Abstract: This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta )$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces. Archive classification: math.FA Submitted from: meimi200(a)postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.3008 or http://arXiv.org/abs/1409.3008

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Abstract of a paper by S Dutta and D Khurana
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "Ordinal indices of small subspaces of $L_p$" by S Dutta and D Khurana. Abstract: We calculate ordinal $L_p$ index defined in "An ordinal L_p index for Banach spaces with an application to complemented subspaces of L_p" authored by J. Bourgain, H. P. Rosenthal and G. Schechtman, for Rosenthal's space $X_p$, $\ell_p$ and $\ell_2$. We show a subspace of $L_p$ $(2 < p < \infty)$ non isomorphic to $\ell_2$ embeds in $\ell_p$ if and only if its ordinal index is minimum possible. We also give a sufficient condition for a $\mathcal{L}_p$ subspace of $\ell_p\oplus\ell_2$ to be isomorphic to $X_p$. Archive classification: math.FA Submitted from: divyakhurana11(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.2330 or http://arXiv.org/abs/1409.2330

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Abstract of a paper by Oleg Reinov
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "O-frames for operators in Banach spaces" by Oleg Reinov. Abstract: These notes are formal. Here, in this abstract, not in the note, we should say that all that is in the text was done, essentially, by Aleksander Pe{\l}czy\'nski. BUT: Anyhow, a new notion of an O-frame for an operator is introduced. For the operators in separable spaces, it is shown that a operator has an O-frame iff it has the BAP iff it can be factored through a Banach space with a basis. Applications are given. However, looking around, I'd say that, e.g., a notion of a Banach frame (and also O-frame) was implicitely introduced by great Aleksander Pe{\l}czy\'nski. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 11 pages, was as a SPb Math. Soc. preprint, in RUSSIAN! Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.0165 or http://arXiv.org/abs/1409.0165

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Abstract of a paper by Valentin Ferenczi and Christian Rosendal
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "Non-unitarisable representations and maximal symmetry" by Valentin Ferenczi and Christian Rosendal. Abstract: We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique invariant complemented subspace. This is subsequently combined with rigidity results for the unitary representation of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite regular tree, to describe the possible bounded subgroups of ${\rm GL}(\mathcal H)$ extending a well-known non-unitarisable representation of $\mathbb F_\infty$. As a related result, we also show that a transitive norm on a separable Banach space must be strictly convex. Archive classification: math.FA Submitted from: rosendal.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.0141 or http://arXiv.org/abs/1409.0141

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