Banach

banach@mathdept.okstate.edu

2549 discussions

Banach spaces webinar Friday 4/3 by Kevin Beanland
by Sari, Bunyamin 30 Mar '20

30 Mar '20

Dear all, The next Banach spaces webinar is on Friday April 3rd 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Kevin Beanland, Washington and Lee Title: Closed ideals of operators on the Tsirelson and Schreier spaces Abstract: Significant progress has been made in our understanding of the lattice of closed ideals of the Banach algebra B(X) of bounded operators on a Banach space X over the last decade. I shall survey some highlights of this development and then focus on the outcomes of an ongoing collaboration with Niels Laustsen (Lancaster University, UK) and Tomasz Kania (Czech Academy of Sciences) in which we study the closed ideals of B(X) in the case where X is either Tsirelson's Banach space or a Schreier space of finite order. Upcoming schedule April 10: Pavlos Motakis, UIUC April 17: Mikhail Ostrovskii, St. John’s April 24: Tomasz Kania, Czech Academy For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Announcement of a Postdoc Position at University of Memphis
by Bentuo Zheng (bzheng) 24 Mar '20

24 Mar '20

Dear All, There will be a two-year postdoc position at the Department of Mathematical Sciences of the University of Memphis which may be renewable for the third year. Please find the details in the attached ad. BR, Bentuo Zheng

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Banach spaces webinar: Friday 3/27 by Ramon van Handel
by Sari, Bunyamin 23 Mar '20

23 Mar '20

Dear all, The next Banach spaces webinar is on Friday 3/27 9AM Central Time. Please join us at https://unt.zoom.us/j/512907580 Speaker: Ramon van Handel, Princeton University. Title: Rademacher type and Enflo type coincide Abstract: A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube. Upcoming schedule April 3: Kevin Beanland, Washington and Lee April 10: Pavlos Motakis, UIUC April 17: Mikhail Ostrovskii, St. John’s April 24: Tomasz Kania, Czech Academy For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Abstract of a paper by Longfa Sun, Yuqi Sun, Wen Zhang, Zheming Zheng
by Bentuo Zheng (bzheng) 01 Mar '20

01 Mar '20

This is an announcement for the paper “On the sum of simultaneously proximinal sets” by Longfa Sun<https://arxiv.org/search/math?searchtype=author&query=Sun%2C+L>, Yuqi Sun<https://arxiv.org/search/math?searchtype=author&query=Sun%2C+Y>, Wen Zhang<https://arxiv.org/search/math?searchtype=author&query=Zhang%2C+W>, Zheming Zheng<https://arxiv.org/search/math?searchtype=author&query=Zheng%2C+Z>. Abstract: In this paper, we show that the sum of a compact convex subset and a simultaneously $\tau$-strongly proximinal convex subset (resp. simultaneously approximatively $\tau$-compact convex subset) of a Banach space X is simultaneously tau-strongly proximinal (resp. simultaneously approximatively $\tau$-compact ), and the sum of weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where $\tau$ is the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented. https://arxiv.org/abs/2002.11961

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Abstract of a paper by Alexandros Eskenazis
by Bentuo Zheng (bzheng) 01 Mar '20

01 Mar '20

This is an announcement for the paper “On Pisier's inequality for UMD targets” by Alexandros Eskenazis<https://arxiv.org/search/math?searchtype=author&query=Eskenazis%2C+A>. Abstract: We prove an extension of Pisier's inequality (1986) with a dimension independent constant for vector valued functions whose target spaces satisfy a relaxation of the UMD property. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.10396

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Abstract of a paper by Javier Merí, Alicia Quero
by Bentuo Zheng (bzheng) 01 Mar '20

01 Mar '20

This is an announcement for the paper “On the numerical index of absolute symmetric norms on the plane” by Javier Merí<https://arxiv.org/search/math?searchtype=author&query=Mer%C3%AD%2C+J>, Alicia Quero<https://arxiv.org/search/math?searchtype=author&query=Quero%2C+A>. Abstract: We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real $L_p$-space for $3/2\leq p\leq 3$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.07529

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Abstract of a paper by Carlo Alberto De Bernardi, Jacopo Somaglia, Libor Vesely
by Bentuo Zheng (bzheng) 01 Mar '20

01 Mar '20

This is an announcement for the paper “Star-finite coverings of Banach spaces” by Carlo Alberto De Bernardi<https://arxiv.org/search/math?searchtype=author&query=De+Bernardi%2C+C+A>, Jacopo Somaglia<https://arxiv.org/search/math?searchtype=author&query=Somaglia%2C+J>, Libor Vesely<https://arxiv.org/search/math?searchtype=author&query=Vesely%2C+L>. Abstract: We study star-finite coverings of infinite-dimensional normed spaces. A family of sets is called star-finite if each of its members intersects only finitely many other members of the family. It follows by our results that an LUR or a uniformly Fréchet smooth infinite-dimensional Banach space does not admit star-finite coverings by closed balls. On the other hand, we present a quite involved construction proving existence of a star-finite covering of $c_0(\Gamma)$ by Fréchet smooth centrally symmetric bounded convex bodies. A similar but simpler construction shows that every normed space of countable dimension (and hence incomplete) has a star-finite covering by closed balls. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.04308

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Abstract of a paper by Morteza Alikhani
by Bentuo Zheng (bzheng) 01 Mar '20

01 Mar '20

This is an announcement for the paper “Factorization Theorem through a Dunford-Pettis $p$-convergent operator” by Morteza Alikhani<https://arxiv.org/search/math?searchtype=author&query=Alikhani%2C+M>. Abstract: In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a factorization result for differentiable mappings through Dunford-Pettis $p$-convergent operators is investigated.\ Namely, if $ X ,Y $ are real Banach spaces and $U$ is an open convex subset of $X,$ then we obtain that, given a differentiable mapping $f: U\rightarrow Y$ its derivative $f^{\prime}$ takes $U$-bounded sets into $p$-$(DPL)$ sets if and only if it happens $f=g\circ S,$ where $S$ is a Dunford-Pettis $p$-convergent operator from $X$ into a suitable Banach space $Z$ and $g:S(U)\rightarrow Y$ is a Gâteaux differentiable mapping with some additional properties. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.01163

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Banach spaces webinars
by Sari, Bunyamin 04 Feb '20

04 Feb '20

Dear Colleague, We are pleased to introduce webinars (online seminars) on Banach spaces and related topics via zoom<https://zoom.us/> on Fridays at 9am central US time. The idea emerged from the fact that there are relatively small number of researchers in the area scattered around the world, and so conducting a regular online seminar where anyone can participate in the convenience of their home makes a lot of sense. How will it work? To participate simply click on the link provided for the seminar and follow instructions. If it is your first time using zoom, you will likely be asked to download the app first. You can click on the link anytime before the meeting to do so. When you join the meeting your microphone is muted by default, so feel free to join anytime there won’t be any unwanted interruptions by doing so. It is interactive; you unmute the mic and ask questions or comments, or click on raise hand button to get speakers’ attention, or chat via on screen text with participants, or simply sit quietly and listen to the talk. Giving a talk is also very easy. It requires minimal tech. For instance, a computer with webcam and Ipad to write on is sufficient. To demonstrate this and to kick off seminars I will give the first talk on this Friday, February 7 at 9am central. Below is the invitation. If you like to speak please send me an email and I will schedule it and help with the set up. Please consider giving a talk and help support webinars keep going. Below is the abstract and invitation of the first talk. Best regards, Bunyamin Sari University of North Texas ____________________________________________ Title: On Sanders’ proof of inequivalence of Walsh and trigonometric systems Abstract. We will speak on Tom Sanders recent proof<https://arxiv.org/abs/1901.03109> that Walsh system in any order is not equivalent to trigonometric basis in $L_p$. The proof uses interesting ideas from additive combinatorics and discrete Fourier analysis which we will present some of the details. _____________________________________________ Bunyamin Sari is inviting you to a scheduled Zoom meeting. Topic: Banach spaces webinar Time: Feb 7, 2020 09:00 AM Central Time (US and Canada) Join Zoom Meeting https://unt.zoom.us/j/353774017 Meeting ID: 353 774 017 One tap mobile +16699006833,,353774017# US (San Jose) +19294362866,,353774017# US (New York) Dial by your location +1 669 900 6833 US (San Jose) +1 929 436 2866 US (New York) Meeting ID: 353 774 017 Find your local number: https://unt.zoom.us/u/appFn0jty Join by SIP 353774017(a)zoomcrc.com<mailto:353774017@zoomcrc.com> Join by H.323 162.255.37.11 (US West) 162.255.36.11 (US East) 221.122.88.195 (China) 115.114.131.7 (India Mumbai) 115.114.115.7 (India Hyderabad) 213.19.144.110 (EMEA) 103.122.166.55 (Australia) 209.9.211.110 (Hong Kong) 64.211.144.160 (Brazil) 69.174.57.160 (Canada) 207.226.132.110 (Japan) Meeting ID: 353 774 017 Join by Skype for Business https://unt.zoom.us/skype/353774017

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Abstract of a paper by Yin-Ting Liao, Kavita Ramanan
by Bentuo Zheng (bzheng) 01 Feb '20

01 Feb '20

This is an announcement for the paper “Geometric sharp large deviations for random projections of $\ell_p^n$ spheres” by Yin-Ting Liao<https://arxiv.org/search/math?searchtype=author&query=Liao%2C+Y>, Kavita Ramanan<https://arxiv.org/search/math?searchtype=author&query=Ramanan%2C+K>. Abstract: Accurate estimation of tail probabilities of projections of high-dimensional probability measures is of relevance in high-dimensional statistics, asymptotic geometric analysis and computer science. For fixed $p \in (1,\infty)$, let $(X^n)_{n \in \mathbb{N}}$ and $(\theta^n)_{n \in \mathbb{N}}$ be independent sequences of random vectors with $X^n$ and $\theta^n$ distributed according to the normalized cone measure on the unit $\ell_p^n$ sphere and $\ell_2^n$ sphere, respectively. For almost every sequence of projection directions $(\theta^n)_{n \in \mathbb{N}}$, (quenched) sharp large deviation estimates are established for suitably normalized (scalar) projections of $X^n$ onto $\theta^n$. In contrast to the (quenched) large deviation rate function, the prefactor is shown to exhibit a dependence on the projection directions that encodes geometric information. Moreover, an importance sampling algorithm is developed to numerically estimate the tail probabilities, and used to illustrate the accuracy of the analytical sharp large deviation estimates for even moderate values of $n$. The results on the one hand provide quantitative estimates of tail probabilities of random projections, valid for finite $n$, generalizing previous results due to Gantert, Kim and Ramanan that characterize only logarithmic asymptotics (as the dimension $n$ tends to infinity), and on the other hand, generalize classical sharp large deviation estimates in the spirit of Bahadur and Ranga Rao to a geometric setting. The proofs combine Fourier analytic and probabilistic techniques, provide a simpler representation for the large deviation rate function that shows that it is strictly convex, and entail establishing central limit theorems for random projections under a certain family of changes of measure, which may be of independent interest. https://arxiv.org/abs/2001.04053

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