Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Antonio Avilés, Pedro Tradacete, Ignacio Villanueva
by Bentuo Zheng (bzheng) 31 Jul '18

31 Jul '18

This is an announcement for the paper “The free Banach lattices generated by $\ell_p$ and $c_0$” by Antonio Avilés<https://arxiv.org/search/math?searchtype=author&query=Avil%C3%A9s%2C+A>, Pedro Tradacete<https://arxiv.org/search/math?searchtype=author&query=Tradacete%2C+P>, Ignacio Villanueva<https://arxiv.org/search/math?searchtype=author&query=Villanueva%2C+I>. Abstract: We prove that, when $2<p<\infty$, in the free Banach lattice generated by $\ell_p$ (respectively by $c_0$), the absolute values of the canonical basis form an $\ell_r$-sequence, where $\frac{1}{r} = \frac{1}{2} + \frac{1}{p}$ (respectively an $\ell_2$-sequence). In particular, in any Banach lattice, the absolute values of any $\ell_p$ sequence always have an upper $\ell_r$-estimate. Quite surprisingly, this implies that the free Banach lattices generated by the nonseparable $\ell_p(\Gamma)$ for $2<p<\infty$, as well as $c_0(\Gamma)$, are weakly compactly generated whereas this is not the case for $1\leq p\leq 2$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1806.02553

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Abstract of a paper by Ben Wallis
by Bentuo Zheng (bzheng) 31 Jul '18

31 Jul '18

This is an announcement for the paper “Closed ideals of operators acting on some families of sequence spaces” by Ben Wallis<https://arxiv.org/search/math?searchtype=author&query=Wallis%2C+B>. Abstract: We study the lattice of closed ideals in the algebra of continuous linear operators acting on $p$th Tandori and $p'$th Ces\`{a}ro sequence spaces, $1\leqslant p<\infty$, which we show are isomorphic to the classical sequence spaces $(\oplus_{n=1}^\infty\ell_\infty^n)_p$ and $(\oplus_{n=1}^\infty\ell_1^n)_{p'}$, respectively. We also show that Tandori sequence spaces are complemented in certain Lorentz sequence spaces, and that the lattice of closed ideals for certain other Lorentz and Garling sequence spaces has infinite cardinality. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1806.00382

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Conference on "Recent Advances in Functional Analysis" dedicated to the memory of Joe Diestel and Victor Lomonosov.
by zvavitch＠math.kent.edu 20 Jun '18

20 Jun '18

Dear Friends, The Analysis group at Kent State University is happy to announce a conference "Recent Advances in Functional Analysis" which will be held at the Department of Mathematical Sciences at Kent State University, Thursday - Sunday, October 11-14, 2018. The conference will be dedicated to the memory of our colleagues and friends Joe Diestel and Victor Lomonosov. Please find current information about participants and the (preliminary) list of speakers at http://www.math.kent.edu/~zvavitch/RAFA2018/ The conference is supported by The Department of Mathematical Sciences and Kent State University and we also have applied for support from NSF. Funding is available to cover the local and travel expenses of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. Please register (over the website) as soon as possible. Note that to receive support and/or help with hotel reservation, you must be registered before September 12, 2018. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format. Finally, please feel free to forward this email to any colleagues or students who you think may be interested in attending. Best regards, The Kent State Analysis Group

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Special issue dedicated to R. G. Douglas
by Bentuo Zheng (bzheng) 20 Jun '18

20 Jun '18

Dear colleague, I would like to invite you to submit a research paper to the issue of Banach J. Math. Anal. dedicated to Professor Ronald G. Douglas for his significant contributions to several mathematics subjects including functional analysis and operator theory. The journal particularly invites research articles within the scope of the journal. There is a restriction on the number of pages of manuscripts: The pages of each paper should be between 14 and 25 in the style of journal. The usual reviewing procedures and standards of BJMA will be applied to all papers for this issue. Preliminary papers or summaries of results previously published are not acceptable. The BJMA is an author-prepared journal which means that authors are responsible for the proper formatting of manuscripts by using its template file. BJMA is published by Duke Univ. Press http://www.projecteuclid.org/euclid.bjma There is no mandatory publication charges for authors and readers in this journal. %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Submission should be done ONLY via the online submission of BJMA at: https://www.editorialmanager.com/bjma/ The deadline for submission is *** 30 September 2018 *** %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Please let the me know ONLY if you are able to have a contribution to this issue (and give me an approximate date for receiving your paper, if possible) by the end of June 2018. Best wishes, M. S. Moslehian (Editor-in-chief ) moslehian(a)yahoo.com<mailto:moslehian@yahoo.com>

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2018 Workshop in Analysis and Probability
by Bentuo Zheng (bzheng) 16 Jun '18

16 Jun '18

Begin forwarded message: From: cara <cara(a)math.tamu.edu<mailto:cara@math.tamu.edu>> Subject: 2018 Workshop in Analysis and Probability Date: June 14, 2018 at 2:47:52 PM CDT To: undisclosed-recipients:; Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2018 The Summer 2018 Workshop in Analysis and Probability at Texas A&M University will be in session from July 2 to August 19. All activities will take place in the Blocker Building. The homepage of the Workshop can be found at http://www.math.tamu.edu/~kerr/workshop<http://www.math.tamu.edu/%7Ekerr/workshop> The Summer Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 17-19. Its homepage is located at http://www.math.tamu.edu/~kerr/workshop/sumirfas2018<http://www.math.tamu.edu/%7Ekerr/workshop/sumirfas2017> August 13-17 there will be a Concentration Week, "Random Walks in Correlated and Dynamic Environments", organized by Eviatar Procaccia and Ron Rosenthal. In recent years great strides have been made in the understanding of random walks in environments more general than the i.i.d. static ones that have been the typical focus of classical investigations. A variety of new developments have spawned a host of open problems, and the time is ripe both for the community to meet and advance the theory and for a new generation of researchers to join the field. To this end, the Concentration Week will provide participants a broad exposure to ideas at the forefront of current research. Given the fact that many of the existing results apply to certain classes of random environments, a particular aim of the meeting will be to promote the search for a more universal understanding of various phenomena across these classes by bringing together specialists working in different subdisciplines. The homepage of the Concentration Week is located at https://sites.google.com/site/rwrecw<http://www.math.tamu.edu/%7Ekerr/etoa2017> The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Starmer <cara(a)math.tamu.edu><mailto:cara@math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu><mailto:johnson@math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu><mailto:kerr@math.tamu.edu>, Gilles Pisier <pisier(a)math.tamu.edu><mailto:pisier@math.tamu.edu>, or Eviatar Procaccia <procaccia(a)math.tamu.edu>.<mailto:lpbowen@math.utexas.edu> For information about the Concentration Week ""Random Walks in Correlated and Dynamic Environments" please contact Eviatar Procaccia <procaccia(a)math.tamu.edu><mailto:lpbowen@math.utexas.edu> or Ron Rosenthal <ron.ro(a)technion.ac.il><mailto:kerr@math.tamu.edu>. -- Cara Barton Program Coordinator Department of Mathematics Texas A&M University College Station, Texas 77843 979-845-2915 (office) 979-845-7554 (department) 979-845-6028 (fax)

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Abstract of a paper by F. Bayart, D. Pellegrino, P. Rueda
by Bentuo Zheng (bzheng) 04 Jun '18

04 Jun '18

This is an announcement for the paper “On coincidence results for summing multilinear operators: interpolation, $\ell_1$-spaces and cotype” by F. Bayart<https://arxiv.org/search?searchtype=author&query=Bayart%2C+F>, D. Pellegrino<https://arxiv.org/search?searchtype=author&query=Pellegrino%2C+D>, P. Rueda<https://arxiv.org/search?searchtype=author&query=Rueda%2C+P>. Abstract: Grothendieck's theorem asserts that every continuous linear operator from $\ell_1$ to $\ell_2$ is absolutely $(1,1)$-summing. This kind of result is commonly called coincidence result. In this paper we investigate coincidence results in the multilinear setting, showing how the cotype of the spaces involved affect such results. The special role played by $\ell_1$ spaces is also investigated with relation to interpolation of tensor products. In particular, an open problem on the interpolation of $m$ injective tensor products is solved. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.12500

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Abstract of a paper by S. J. Dilworth, Divya Khurana
by Bentuo Zheng (bzheng) 04 Jun '18

04 Jun '18

This is an announcement for the paper “Characterizations of almost greedy and partially greedy bases” by S. J. Dilworth<https://arxiv.org/search?searchtype=author&query=Dilworth%2C+S+J>, Divya Khurana<https://arxiv.org/search?searchtype=author&query=Khurana%2C+D>. Abstract: We shall present new characterizations of partially greedy and almost greedy bases. A new class of basis (which we call reverse partially greedy basis) arises naturally from these characterizations of partially greedy bases. We also give characterizations for $1$-partially greedy and $1$-reverse partially greedy bases. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.06778

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Abstract of a paper by Yunan Cui, Henryk Hudzik, Haifeng Ma
by Bentuo Zheng (bzheng) 04 Jun '18

04 Jun '18

This is an announcement for the paper “Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$” by Yunan Cui<https://arxiv.org/search?searchtype=author&query=Cui%2C+Y>, Henryk Hudzik<https://arxiv.org/search?searchtype=author&query=Hudzik%2C+H>, Haifeng Ma<https://arxiv.org/search?searchtype=author&query=Ma%2C+H>. Abstract: In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$) studied in [10-11], [14-15] and [20]. Criteria for strict monotonicity, lower and upper local uniform monotonicities and uniform monotonicities of Orlicz spaces and their subspaces of order continuous elements, equipped with these norms, are given in terms of the generating Orlicz functions, and the lattice norm in $\mathbb{R}^{2}$. The problems of strict convexity and of the existence of order almost isometric as well as of order isometric copies in these spaces are also discussed. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.06720

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Abstract of a paper by Maciej Ciesielski, Grzegorz Lewicki
by Bentuo Zheng (bzheng) 04 Jun '18

04 Jun '18

This is an announcement for the paper “Sequence Lorentz spaces and their geometric structure” by Maciej Ciesielski<https://arxiv.org/search?searchtype=author&query=Ciesielski%2C+M>, Grzegorz Lewicki<https://arxiv.org/search?searchtype=author&query=Lewicki%2C+G>. Abstract: This article is dedicated to geometric structure of the Lorentz and Marcinkiewicz spaces in case of the pure atomic measure. We study complete criteria for order continuity, the Fatou property, strict monotonicity and strict convexity in the sequence Lorentz spaces $\gamma_{p,w}$. Next, we present a full characterization of extreme points of the unit ball in the sequence Lorentz space $\gamma_{1,w}$. We also establish a complete description with an isometry of the dual and predual spaces of the sequence Lorentz spaces $\gamma_{1,w}$ written in terms of the Marcinkiewicz spaces. Finally, we show a fundamental application of geometric structure of $\gamma_{1,w}$ to one-complemented subspaces of $\gamma_{1,w}$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.06355

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Abstract of a paper by Miguel Martin
by Bentuo Zheng (bzheng) 04 Jun '18

04 Jun '18

This is an announcement for the paper “On proximinality of subspaces of finite codimension of Banach spaces and the lineability of the set of norm-attaining functionals” by Miguel Martin<https://arxiv.org/search?searchtype=author&query=Martin%2C+M>. Abstract: We show that for every $1<n<\infty$, there exits a Banach space $X_n$ containing proximinal subspaces of codimension $n$ but no proximinal finite codimensional subspaces of higher codimension. Moreover, the set of norm-attaining functionals of $X_n$ contains $n$-dimensional subspaces, but no subspace of higher dimension. This gives a $n$-by-$n$ version of the solutions given by Read and Rmoutil to problems of Singer and Godefroy. Actually, the space $X_n$ can be found with strictly convex dual and bidual, and such that the slices of its unit ball have diameter as close to two as desired. We also deal with the existence of strongly proximinal subspaces of finite codimension, showing that for every $1<n<\infty$ and $1\leq k <n$, there is a Banach space $X_{n,k}$ containing proximinal subspaces of finite codimension up to $n$ but not higher, and containing strongly proximinal subspaces of finite codimension up to $k$ but not higher. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.05979

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