Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Matthew Tarbard
by alspach＠math.okstate.edu 15 Oct '13

15 Oct '13

This is an announcement for the paper "Operators on Banach spaces of Bourgain-Delbaen type" by Matthew Tarbard. Abstract: We begin by giving a detailed exposition of the original Bourgain-Delbaen construction and the generalised construction due to Argyros and Haydon. We show how these two constructions are related, and as a corollary, are able to prove that there exists some $\delta > 0$ and an uncountable set of isometries on the original Bourgain-Delbaen spaces which are pairwise distance $\delta$ apart. We subsequently extend these ideas to obtain our main results. We construct new Banach spaces of Bourgain-Delbaen type, all of which have $\ell_1$ dual. The first class of spaces are HI and possess few, but not very few operators. We thus have a negative solution to the Argyros-Haydon question. We remark that all these spaces have finite dimensional Calkin algebra, and we investigate the corollaries of this result. We also construct a space with $\ell_1$ Calkin algebra and show that whilst this space is still of Bourgain-Delbaen type with $\ell_1$ dual, it behaves somewhat differently to the first class of spaces. Finally, we briefly consider shift-invariant $\ell_1$ preduals, and hint at how one might use the Bourgain-Delbaen construction to produce new, exotic examples. Archive classification: math.FA Remarks: Oxford University DPhil Thesis Submitted from: matthew.tarbard(a)sjc.ox.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.7469 or http://arXiv.org/abs/1309.7469

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Conference Announcement - First Brazilian Workshop in Geometry of Banach Spaces: August 2014
by valentin ferenczi 07 Oct '13

07 Oct '13

1st ANNOUNCEMENT OF BWB 2014 First Brazilian Workshop in Geometry of Banach Spaces August 25-29, 2014 Maresias, São Paulo State, Brazil. This is the 1st 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. The webpage of the Workshop may be found at http://www.ime.usp.br/~banach/bwb2014/ Registration will start in early 2014. Additional scientific, practical and financial information will be given at that time. 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) 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) We are looking forward to meeting you next year in Brazil, F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.

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Abstract of a paper by Vitalii Marchenko
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Isomorphic Schauder decompositions in certain Banach spaces" by Vitalii Marchenko. Abstract: We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use $\ell_{\Psi}$-Hilbertian and $\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition in a Hilbert space and introduce the class of spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and $M$-cotype of a Banach space and study the properties of unconditional Schauder decompositions in spaces possessing certain geometric structure. Archive classification: math.FA Mathematics Subject Classification: 47A46, 46B15, 47B40 Remarks: 35 pages Submitted from: vitalii.marchenko(a)karazin.ua The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.6552 or http://arXiv.org/abs/1309.6552

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Abstract of a paper by Benoit Collins, Piotr Gawron, Alexander E. Litvak, and Karol Zyczkowski
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Numerical range for random matrices" by Benoit Collins, Piotr Gawron, Alexander E. Litvak, and Karol Zyczkowski. Abstract: We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. We show that the numerical range of complex Ginibre ensemble converges to the disk of radius $\sqrt{2}$. Since the spectrum of non-hermitian random matrices from the Ginibre ensemble lives asymptotically in a neighborhood of the unit disk, it follows that the outer belt of width $\sqrt{2}-1$ containing no eigenvalues can be seen as a quantification the non-normality of the complex Ginibre random matrix. We also show that the numerical range of upper triangular Gaussian matrices converges to the same disk of radius $\sqrt{2}$, while all eigenvalues are equal to zero and we prove that the operator norm of such matrices converges to $\sqrt{2e}$. Archive classification: math.OA math.FA math.PR quant-ph Mathematics Subject Classification: 5A60, 47A12, 15B52 (primary), 46B06, 60B20 (secondary) Remarks: 22 pages, 4 figures Submitted from: gawron(a)iitis.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.6203 or http://arXiv.org/abs/1309.6203

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Abstract of a paper by Veronica Dimant and Pablo Sevilla-Peris
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Summation of coefficients of polynomials on $\ell_{p}$ spaces" by Veronica Dimant and Pablo Sevilla-Peris. Abstract: We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our research we obtain results on the summability of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times \cdots \times \ell_{p_{m}}$. The first results in this respect go back to Littlewood and Bohnenblust and Hille (for bilinear and $m$-linear forms on $c_{0}$) and Hardy and Littlewood and Praciano-Pereira (for bilinear and $m$-linear forms on arbitrary $\ell_{p}$-spaces). Our results recover and in some case complete these old results through a general approach on vector valued $m$-linear mappings. Archive classification: math.FA Submitted from: psevilla(a)mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.6063 or http://arXiv.org/abs/1309.6063

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Abstract of a paper by Daniel J. Fresen
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Euclidean grid structures in Banach spaces" by Daniel J. Fresen. Abstract: We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Kashin decomposition. Archive classification: math.FA Mathematics Subject Classification: 46B20, 52A23, 46B09, 52A21, 46B07 Remarks: 16 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/1309.5526 or http://arXiv.org/abs/1309.5526

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Abstract of a paper by T. Oikhberg and E. Spinu
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Operator ideals on non-commutative function spaces" by T. Oikhberg and E. Spinu. Abstract: Suppose $X$ and $Y$ are Banach spaces, and ${\mathcal{I}}$, ${\mathcal{J}}$ are operator ideals (for instance, the ideals of strictly singular, weakly compact, or compact operators). Under what conditions does the inclusion ${\mathcal{I}}(X,Y) \subset {\mathcal{J}}(X,Y)$, or the equality ${\mathcal{I}}(X,Y) = {\mathcal{J}}(X,Y)$, hold? We examine this question when ${\mathcal{I}}, {\mathcal{J}}$ are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while $X$ and $Y$ are non-commutative function spaces. Since such spaces are ordered, we also address the same questions for positive parts of such ideals. Archive classification: math.OA Submitted from: spinu(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.5434 or http://arXiv.org/abs/1309.5434

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Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "Extreme differences between weakly open subsets and convex of slices in Banach spaces" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca. Abstract: We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and, however, its unit ball still contains convex combinations of slices with diameter arbitrarily small, which improves in a optimal way the known results about the size of this kind of subsets in Banach spaces. Archive classification: math.FA Submitted from: glopezp(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.4950 or http://arXiv.org/abs/1309.4950

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Abstract of a paper by D.I. Florentin, V.D. Milman, and R. Schneider
by alspach＠math.okstate.edu 30 Sep '13

30 Sep '13

This is an announcement for the paper "A characterization of the mixed discriminant" by D.I. Florentin, V.D. Milman, and R. Schneider. Abstract: We characterize the mixed discriminant of positive semi definite matrices using its most basic properties. As a corollary we establish its minimality among non negative and multi additive functionals. Archive classification: math.FA Submitted from: danflorentin(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.4798 or http://arXiv.org/abs/1309.4798

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Abstract of a paper by Spiros Argyros, Kevin Beanland and Pavlos Motakis(Correction)
by Dale Alspach 30 Sep '13

30 Sep '13

The URLs were wrong in the previous email. This is an announcement for the paper "Strictly singular operators in Tsirelson like spaces" by Spiros Argyros, Kevin Beanland and Pavlos Motakis. Abstract: For each $n \in \mathbb{N}$ a Banach space $\mathfrak{X}_{0,1}^n$ is constructed is having the property that every normalized weakly null sequence generates either a $c_0$ or $\ell_1$ spreading models and every infinite dimensional subspace has weakly null sequences generating both $c_0$ and $\ell_1$ spreading models. The space $\mathfrak{X}_{0,1}^n$ is also quasiminimal and for every infinite dimensional closed subspace $Y$ of $\mathfrak{X}_{0,1}^n$, for every $S_1,S_2,\ldots,S_{n+1}$ strictly singular operators on $Y$, the operator $S_1S_2\cdots S_{n+1}$ is compact. Moreover, for every subspace $Y$ as above, there exist $S_1,S_2,\ldots,S_n$ strictly singular operators on $Y$, such that the operator $S_1S_2\cdots S_n$ is non-compact. Archive classification: math.FA Remarks: 45 pages Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.4516 or http://arXiv.org/abs/1309.4516

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