Banach

banach@mathdept.okstate.edu

2549 discussions

Announcement of Papers in August, 2020
by Bentuo Zheng (bzheng) 02 Sep '20

02 Sep '20

Dear Subscribers, Please check the following link for updated list of papers in August, 2020. https://bentuo.wixsite.com/banach/banach-space-bulletin-board Bentuo Zheng Professor, Department of Mathematical Sciences, University of Memphis

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Announcement of Papers in August, 2020
by Bentuo Zheng (bzheng) 02 Sep '20

02 Sep '20

Dear Subcribers, Please check the following link for updated list of papers in August, 2020. Best, Bentuo Zheng Professor, Department of Mathematical Sciences, College of Arts and Sciences

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Banach spaces webinar on Friday Aug 28 by Tommaso Russo (Czech Academy of Sciences and Czech Technical University in Prague)
by Sari, Bunyamin 25 Aug '20

25 Aug '20

Dear all, The next Banach spaces webinar is on Friday August 28 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Tommaso Russo (Czech Academy of Sciences and Czech Technical University in Prague) Title: Asplund Banach spaces with norming Markuševič bases Abstract The first existence result for norming Markuševič bases (M-bases, for short) in Banach spaces is perhaps due to Markuševič, who proved that every separable Banach space admits a 1-norming M-basis. After the introduction of projectional resolutions of the identity, it became clear that such bases also exist in every reflexive Banach space. In order to understand the strength of the said notion, a natural problem at the time was then to characterise those (non-separable) Banach spaces that admit a norming M-basis. Perhaps the main question, due originally to John and Zizler and that was solved very recently by P. Hájek, was whether every weakly compactly generated (WCG) Banach space admits a norming M-basis. In the converse direction, it was asked by Gilles Godefroy if an Asplund space with a norming M-basis is necessarily WCG. In the talk, based on a joint work with P. Hájek, J. Somaglia, and S. Todorčević, we shall discuss our recent negative answer to the latter question. Moreover, the construction yields an interesting example of a scattered compact space that also solves a question due to Wiesław Kubiś and Arkady Leiderman. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule September 4: Mary Angelica Tursi (UIUC) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday August 21 by Khazhak Navoyan (Thompson Rivers University)
by Sari, Bunyamin 17 Aug '20

17 Aug '20

Dear all, The next Banach spaces webinar is on Friday August 21 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Khazhakanush Navoyan (Thompson Rivers University) Title: The positive Schur property on spaces of regular multilinear operators Abstract In this paper we give necessary and sufficient conditions for the space of regular multilinear operators from the product of Banach lattices to a Dedekind complete Banach lattice to have the positive Schur property. We also characterize the positive Schur property on the positive projective $m$-fold tensor product of Banach lattices, $m \in \mathbb{N}$, and on its dual. This is a joint work with Geraldo Botelho, Qingying Bu and Donghai Ji. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule August 28: Tommaso Russo (Czech Technical University) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday August 14 by Robert Young (NYU)
by Sari, Bunyamin 11 Aug '20

11 Aug '20

Dear all, The next Banach spaces webinar is on Friday August 14 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Robert Young (NYU) Title: Metric differentiation and Lipschitz embeddings in $L_p$ spaces Abstract Kadec and Pełczyński showed that if $1\le p\lt 2\lt q\lt \infty$ and $X$ is a Banach space that embeds into both $L_p$ and $L_q$, then $X$ is isomorphic to a Hilbert space. The search for metric analogues of such a result is intertwined with the Ribe program and metric theories of type and cotype. Recently, with Assaf Naor, we have constructed a metric space based on the Heisenberg group which embeds into $L_1$ and $L_4$ but not in $L_2$. In this talk, we will describe this example, explain why embeddings of the Heisenberg group into Banach spaces must be "bumpy" at many scales, and discuss how to bound the bumpiness of Lipschitz maps to Banach spaces. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule August 21: Gilles Pisier (TAMU) Thank you, and best regards, Bunyamin Sari

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Postdoc Position at University of Memphis
by Bentuo Zheng (bzheng) 10 Aug '20

10 Aug '20

Dear Subscribers, This is an announcement for a two-year postdoc position (with the possibility of renewal for the third year) at University of Memphis. Functional Analysis is one of our preferred areas. Please find the details at the following link: https://workforum.memphis.edu/postings/25767 Since the time frame for the application is relatively short, we encourage eligible candidates to apply as soon as possible. Best regards, Bentuo Zheng Professor, Department of Mathematical Sciences, College of Arts and Sciences [UofM logo] The University of Memphis 359 Dunn Hall Memphis, TN 38152<http://www.memphis.edu/emailsignatures/emailsignaturemac.php#> 901.678<http://www.memphis.edu/emailsignatures/emailsignaturemac.php#>.3534 | memphis.edu<http://www.memphis.edu/>

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Banach spaces webinar on Friday August 7 by Pete Casazza
by Sari, Bunyamin 03 Aug '20

03 Aug '20

Dear all, The next Banach spaces webinar is on Friday August 7 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Pete Casazza (University of Missouri) Title: Tsirelson space, explicitly definable Banach space, implicitly definable Banach space Abstract. We prove that Tsirelson's space cannot be defined explicitly from the classical Banach sequence spaces. We also prove that any Banach space that is explicitly definable from a class of spaces that contain $\ell_p$ or $c_0$ must contain $\ell_p$ or $c_0$ as well. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule August 14: Robert Young (NYU) Thank you, and best regards, Bunyamin Sari

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Updated list of papers for July 2020
by Bentuo Zheng (bzheng) 01 Aug '20

01 Aug '20

Dear Subscribers, Please check the following link for updated list of papers for July 2020. https://bentuo.wixsite.com/banach/banach-space-bulletin-board MOST RECENT PREPRINTS | Banach<https://bentuo.wixsite.com/banach/banach-space-bulletin-board> Most Recent Preprints. June, 2020. Rosenthal's space revisited by Sergey V. Astashkin, Guillermo P. Curbera.. Reflexive Banach spaces with all power-bounded operators ... bentuo.wixsite.com

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Banach spaces webinar on Friday July 31 by Valentin Ferenczi
by Sari, Bunyamin 27 Jul '20

27 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 31 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Valentin Ferenczi (University of São Paulo) Title: On envelopes and L_p-spaces Abstract. This talk is based on a work in progress with Jordi Lopez-Abad. We define, inside a given space $X$, the {\em envelope} ${\rm Env}(Y)$ of a subspace $Y$ as the largest subspace such that, for any net of surjective isometries on $X$, pointwise convergence to the identity on $Y$ implies pointwise convergence to the identity on ${\rm Env}(Y)$. This is reminiscent of the study of Korovkin sets in the spaces $C(0,1)$ or $L_p(\mu)$ (initiated by P.P. Korovkin in 1960). We shall mention some results of a recent paper of J. Lopez-Abad, B. Mbombo, and S. Todorcevic and myself (2019): different notions of ultrahomogeneity of Banach spaces will be stated (AUH, Fra\"iss\'e) which are relevant to multidimensional versions of Mazur rotations problem. Known examples of these are the Gurarij space and the spaces $L_p$'s for $p \neq 4,6,8,\ldots$. We shall address the conjecture that these are the only separable examples. The notion of envelope is especially relevant to the study of AUH or Fra\"iss\'e spaces. In particular we shall compute explicitely certain envelopes in $L_p$-spaces and conclude by giving a meaning to potentially new objects such as $L_p/\ell_2$, $L_p/L_q$, $L_p/\ell_q$, for appropriate values of $p$ and $q$. Partially supported by Fapesp, 2016/25574-8 and CNPq, 303731/2019-2. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule August 7: Pete Casazza (University of Missouri) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday July 24 by Florent Baudier
by Sari, Bunyamin 21 Jul '20

21 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 24 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Florent Baudier (Texas A&M) Title: L_1-embeddability of lamplighter metrics Abstract. Lamplighter groups are important and well-studied objects in (geometric) group theory as they provide examples of groups with a variety of interesting geometric/algebraic properties. The lamplighter construction can naturally be extended to apply to graphs and is instrumental in the study of random walks on graphs. However, much remains to be understood regarding the embeddability of lamplighters groups or graphs into classical Banach spaces. Inspired by works on the earthmover distance I will explain how the machinery of stochastic embeddings into tree metrics can be fruitfully applied to the study of L_1-embeddability of lamplighter metrics and how it provides general upper bounds on the L_1-distortion of finite lamplighter graphs (and groups). I will then discuss an application to the coarse embeddability of the planar lamplighter group and if time permits an application to linear embeddings of Arens-Eells spaces over finite metric spaces into finite-dimensional l_1-spaces. The talk will be targeted towards non-specialists. Based on joint works with P. Motakis (UIUC), Th. Schlumprecht (Texas A&M), and A. Zsák (Peterhouse, Cambridge) * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 31: Valentin Ferenczi (University of São Paulo) Thank you, and best regards, Bunyamin Sari

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