Banach

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Abstract of a paper by Ian Doust, Stephen Sanchez and Anthony Weston
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "The generalized roundness of $\ell_\infty^{(3)}$ revisited" by Ian Doust, Stephen Sanchez and Anthony Weston. Abstract: Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p \leq 2$. Lennard, Tonge and Weston gave an indirect proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero by appealing to highly non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this paper we give a direct proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero. This provides insight into the combinatorial geometry of $\ell_{\infty}^{(3)}$ that causes the generalized roundness inequalities to fail. We complete the paper by noting a characterization of real quasi-normed spaces of generalized roundness zero. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 8 pages Submitted from: i.doust(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.4095 or http://arXiv.org/abs/1401.4095

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Abstract of a paper by Rainis Haller and Johann Langemets
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Geometry of Banach spaces with an octahedral norm" by Rainis Haller and Johann Langemets. Abstract: We discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering of the unit ball. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Submitted from: johann.langemets(a)ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.3612 or http://arXiv.org/abs/1401.3612

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Abstract of a paper by Tim de Laat and Mikael de la Salle
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Strong property (T) for higher rank simple Lie groups" by Tim de Laat and Mikael de la Salle. Abstract: We prove that connected higher rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces $\mathcal{E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as well. This generalizes the result of Lafforgue asserting that $\mathrm{SL}(3,\mathbb{R})$ has strong property (T) with respect to Hilbert spaces and the more recent result of the second named author asserting that $\mathrm{SL}(3,\mathbb{R})$ has strong property (T) with respect to a certain larger class of Banach spaces. For the generalization to higher rank groups, it is sufficient to prove strong property (T) for $\mathrm{Sp}(2,\mathbb{R})$ and its universal covering group. As consequences of our main result, it follows that for $X \in \mathcal{E}_{10}$, connected higher rank simple Lie groups and their lattices have property (F$_X$) of Bader, Furman, Gelander and Monod, and the expanders contructed from a lattice in such a group do not admit a coarse embedding into $X$. Archive classification: math.GR math.FA math.MG Report Number: CPH-SYM-DNRF92 Remarks: 30 pages, 1 figure Submitted from: tim.delaat(a)wis.kuleuven.be The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.3611 or http://arXiv.org/abs/1401.3611

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Abstract of a paper by Dusan Repovs and Pavel V. Semenov
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Continuous selections of multivalued mappings" by Dusan Repovs and Pavel V. Semenov. Abstract: This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume. Archive classification: math.GN math.FA math.GT math.OC Mathematics Subject Classification: 54C60, 54C65, 28B20, 26E25, 49J53, 58C06 Citation: Recent Progress in General Topology III, (K. P. Hart, Jan van The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.2257 or http://arXiv.org/abs/1401.2257

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Abstract of a paper by Andrzej Wisnicki
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Hyper-extensions in metric fixed point theory" by Andrzej Wisnicki. Abstract: We apply a modern axiomatic system of nonstandard analysis in metric fixed point theory. In particular, we formulate a nonstandard iteration scheme for nonexpansive mappings and present a nonstandard approach to fixed-point problems in direct sums of Banach spaces. Archive classification: math.FA math.LO Remarks: 12 pages 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/1401.2144 or http://arXiv.org/abs/1401.2144

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Abstract of a paper by Dale E. Alspach and Eloi Medina Galego
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "A complete classification of the spaces of compact operators on C([1,alpha], l_p) spaces, 1<p< infinity" by Dale E. Alspach and Eloi Medina Galego. Abstract: We complete the classification, up to isomorphism, of the spaces of compact operators on C([1, gamma], l_p) spaces, 1<p< infinity. In order to do this, we classify, up to isomorphism, the spaces of compact operators {\mathcal K}(E, F), where E= C([1, lambda], l_p) and F=C([1,xi], l_q) for arbitrary ordinals lambda and xi and 1< p \leq q< infinity. More precisely, we prove that it is relatively consistent with ZFC that for any infinite ordinals lambda, mu, xi and eta the following statements are equivalent: (a) {\mathcal K}(C([1, lambda], l_p), C([1, xi], l_q)) is isomorphic to {\mathcal K}(C([1, mu], l_p), C([1, eta], l_q)) . (b) lambda and mu have the same cardinality and C([1,xi]) is isomorphic to C([1, eta]) or there exists an uncountable regular ordinal alpha and 1 \leq m, n < omega such that C([1, xi]) is isomorphic to C([1, alpha m]) and C([1,eta]) is isomorphic to C([1, alpha n]). Moreover, in ZFC, if lambda and mu are finite ordinals and xi and eta are infinite ordinals then the statements (a) and (b') are equivalent. (b') C([1,xi]) is isomorphic to C([1, eta]) or there exists an uncountable regular ordinal alpha and 1 \leq m, n \leq omega such that C([1, xi]) is isomorphic to C([1, alpha m]) and C([1,eta]) is isomorphic to C([1, alpha n]). Archive classification: math.FA Mathematics Subject Classification: 46B03 (primary) 46B25 (secondary) Remarks: Revised version will appear in Proc. AMS Submitted from: alspach(a)math.okstate.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.1857 or http://arXiv.org/abs/1401.1857

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Abstract of a paper by Wilson Cuellar-Carrera
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "A Banach space with a countable infinite number of complex structures" by Wilson Cuellar-Carrera. Abstract: We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures. Archive classification: math.FA Submitted from: cuellar(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.1781 or http://arXiv.org/abs/1401.1781

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Abstract of a paper by Fernando Albiac and Jose L. Ansorena
by alspach＠math.okstate.edu 17 Jan '14

17 Jan '14

This is an announcement for the paper "Non-existence of greedy bases in direct sums of mixed $\ell_{p}$ spaces" by Fernando Albiac and Jose L. Ansorena. Abstract: The fact that finite direct sums of two or more mutually different spaces from the family $\{\ell_{p} : 1\le p<\infty\}\cup c_{0}$ fail to have greedy bases is stated in [Dilworth et al., Greedy bases for Besov spaces, Constr. Approx. 34 (2011), no. 2, 281-296]. However, the concise proof that the authors give of this fundamental result in greedy approximation relies on a fallacious argument, namely the alleged uniqueness of unconditional basis up to permutation of the spaces involved. The main goal of this note is to settle the problem by providing a correct proof. For that we first show that all greedy bases in an $\ell_{p}$ space have fundamental functions of the same order. As a by-product of our work we obtain that {\it every} almost greedy basis of a Banach space with unconditional basis and nontrivial type contains a greedy subbasis. Archive classification: math.FA Mathematics Subject Classification: 41A35, 46B15 46B45, 46T99 Submitted from: joseluis.ansorena(a)unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0693 or http://arXiv.org/abs/1401.0693

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Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski
by Jose Rodriguez 15 Jan '14

15 Jan '14

Dear colleagues: This is the second announcement of the conference Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski which will be held in Albacete (Spain) on June 10-13, 2014, on the occasion of the 70th birthday of Professor Troyanski. Our web page at https://sites.google.com/site/geometryofbanachspaces/ contains detailed information about the conference. Main speakers who accepted our invitation are: S. Argyros, J. Castillo, S. Dilworth, M. Fabian, V. Fonf, G. Godefroy, P. Hajek, R. Haydon, F. Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, T. Schlumprecht, R. Smith, A. Suarez Granero. Registration is OPEN. Participants must pay a fee which will cover conference materials, lunches and coffee breaks during the conference. Details about the payment can be found in our web page. - Deadline for early registration: April 30. - Deadline for late registration: May 31. Participants will have the opportunity to deliver a short talk. The deadline for abstract submission is May 15. Accommodation: the conference web page includes a list of hotels in Albacete offering special rates for the participants. Please do not hesitate in contacting us at geometry.banach.spaces.2014(a)gmail.com if you need further information. Looking forward to meeting you! The organizers, A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez.

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Abstract of a paper by D. Carando, S. Lassalle, and M. Mazzitelli
by alspach＠math.okstate.edu 04 Jan '14

04 Jan '14

This is an announcement for the paper "A Lindenstrauss theorem for some classes of multilinear mappings" by D. Carando, S. Lassalle, and M. Mazzitelli. Abstract: Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their norms. We also consider the class of symmetric multilinear mappings. Archive classification: math.FA Remarks: 11 pages Submitted from: mmazzite(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0488 or http://arXiv.org/abs/1401.0488

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