Banach

banach@mathdept.okstate.edu

2549 discussions

Banach spaces webinar on Friday October 9 by Vladimir Temlyakov (University of South Carolina)
by Sari, Bunyamin 05 Oct '20

05 Oct '20

Dear all, The next Banach spaces webinar is on Friday October 9 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Vladimir Temlyakov, University of South Carolina Title: Sampling discretization of integral norms Abstract: The talk is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this talk we discuss a conditional theorem for all integral norms $L_q$, $1\le q<\infty$. A new technique, which works well for discretization of the integral norms, was used. It is a combination of probabilistic technique with results on the entropy numbers in the uniform norm. We discuss the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensional subspace. As an application of the general conditional theorem, we discuss a new Marcinkiewicz type discretization for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. It is shown that recently developed techniques allow us to improve the known results in this direction. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday October 2 by Anna Pelczar-Barwacz (Jagiellonian University)
by Sari, Bunyamin 30 Sep '20

30 Sep '20

Dear all, The next Banach spaces webinar is on Friday October 2 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Anna Pelczar-Barwacz, Jagiellonian University Title: Small operator ideals on the Schlumprecht and Schreier spaces Abstract. I report on the joint work with Antonis Manoussakis, showing that there are $2^{2^{\aleph_0}}$ many different closed operator ideals on the Schlumprecht space and every Schreier space of finite order admits a chain of the cardinality $2^{\aleph_0}$ of closed operator ideals. 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 October 9: Vladimir Temlyakov, University of South Carolina Thank you, and best regards, Bunyamin Sari

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Correction
by Bentuo Zheng (bzheng) 27 Sep '20

27 Sep '20

The correct date for VOTCAM 2020 is October 3rd. Ben

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VOTCAM 2020
by Bentuo Zheng (bzheng) 27 Sep '20

27 Sep '20

Dear Subscribers, This is a reminder that VOTCAM 2020 will be held on October 1st. Please check the following link for details. https://mailchi.mp/3908f7b0638f/votcam-2020-on-zoom?e=0bfb46bf45 Best, Bentuo Zheng Professor, Department of Mathematical Sciences, College of Arts and Sciences, University of Memphis

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Banach spaces webinar on Friday Sep 25 by Paata Ivanisvili (North Carolina State)
by Sari, Bunyamin 22 Sep '20

22 Sep '20

Dear all, The next Banach spaces webinar is on Friday September 25 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Paata Ivanisvili North Carolina State Title: Sharpening the triangle inequality in Lp spaces Abstract. The classical triangle inequality in Lp estimates the norm of the sum of two functions in terms of the sums of the norms of these functions. Perhaps one drawback of this estimate is that it does not see how "orthogonal" these functions are. For example, if f and g are not identically zero and they have disjoint supports then the triangle inequality is pretty strict (say for p>1). Motivated by the L2 case, where one has a trivial inequality ||f+g||^2 \leq ||f||^2 + ||g||^2 + 2 |fg|_1, one can think about the quantity |fg|_1 as measuring the "overlap" between f and g. What is the correct analog of this estimate in Lp for p different than 2? My talk will be based on a joint work with Carlen, Frank and Lieb where we obtain one extension of this estimate in Lp, thereby proving and improving the suggested possible estimates by Carbery, and another work with Mooney where we further refine these estimates. The estimates will be provided for all real p's. * 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 October 2: Anna Pelczar-Barwacz, Jagiellonian University Thank you, and best regards, Bunyamin Sari

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Operator Theory Seminar at the University of Virginia
by Braga 17 Sep '20

17 Sep '20

Dear Banach Space-natics, I am sending this email to advertise the Online Operator Theory Seminar at the University of Virginia. Because of the current pandemic, our seminar is happening online on Zoom. In case you would like to receive weekly emails with information about the seminar (including speaker, title, abstract and Zoom link), please send me an email to demendoncabraga(a)gmail.com. With a few exceptions, the Operator Theory Seminar at UVA happens every Tuesday at 3:45 PM (US Eastern Standard Time). If the speaker agrees, the talks are recorded and posted on YouTube. Here is the link for our channel: https://www.youtube.com/channel/UCtWmTsY1I0Te0aFw_gGqo-A Our next seminar is on September 22nd (next Tuesday) at 4:00 PM (not at 3:45 PM as usual!). Our speaker is Javier Alejandro Chávez-Domínguez from University of Oklahoma and here are his title and abstract: Title: Asymptotic dimension and coarse embeddings in the quantum setting Abstract: We generalize the notions of asymptotic dimension and coarse embeddings from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that quantum asymptotic dimension behaves well with respect to metric quotients, direct sums, and quantum coarse embeddings. Moreover, we prove that a quantum metric space that equi-coarsely contains a sequence of reflexive quantum expanders must have infinite asymptotic dimension. This is done by proving a vertex-isoperimetric inequality for quantum expanders, based upon a previously known edge-isoperimetric one due to Temme, Kastoryano, Ruskai, Wolf, and Verstraete. Joint work with Andrew Swift. You can access the talk at the following link: https://virginia.zoom.us/j/94431300866?pwd=M1c2UU41R0lDemVvdDBWb1JvZytWUT09 I hope you all have a nice week. Cheers, Braga

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Banach spaces webinar on Friday Sep 18 by Chris Phillips (University of Oregon)
by Sari, Bunyamin 15 Sep '20

15 Sep '20

Dear all, The next Banach spaces webinar is on Friday September 18 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Chris Phillips, University of Oregon Title: Operator algebras on L^p spaces Abstract. Surprisingly, there appears to be a rich theory of "C* like" operator algebras on L^p spaces. It is far from actual C*-algebras, but analogs of some of the basic examples of C*-algebras have analogs on L^p spaces which share at least some of the properties of the C* examples. Some of the methods of proof are very different. There are many open problems. We do not even have a definition of what it means for an L^p operator algebra to be "C* like"--just some heuristic criteria. This talk will try to give an impression of the current state of the theory, focusing on several classes of examples. It will not assume significant knowledge of C*-algebras. * 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 25: Paata Ivanisvili North Carolina State Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday Sep 11 by Bence Horváth (Czech Academy of Sciences)
by Sari, Bunyamin 09 Sep '20

09 Sep '20

Dear all, The next Banach spaces webinar is on Friday September 11 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Bence Horváth, Czech Academy of Sciences Title: When are surjective algebra homomorphisms of $\mathcal{B}(X)$ automatically injective? Abstract. A classical result of Eidelheit asserts that if $X$ and $Y$ are Banach spaces then they are isomorphic if and only if their algebras of operators $\mathcal{B}(X)$ and $\mathcal{B}(Y)$ are isomorphic as Banach algebras, in the sense that there is a continuous bijective algebra homomorphism $\psi: \, \mathcal{B}(X) \rightarrow \mathcal{B}(Y)$. It is natural to ask whether for some class of Banach spaces $X$ this theorem can be strengthened in the following sense: If $Y$ is a non-zero Banach space and $\psi: \mathcal{B}(X) \rightarrow \mathcal{B}(Y)$ is a surjective algebra homomorphism, is $\psi$ automatically injective? It is easy to see that for a ``very nice'' class Banach spaces, such as $c_0$ and $\ell_p$, where $1 \leq p < \infty$, the answer is positive. Further examples include $\ell_{\infty}$ and $( \oplus_{n=1}^{\infty} \ell_2^n )_{c_0}$ and its dual space $\left( \oplus_{n=1}^{\infty} \ell_2^n \right)_{\ell_1}$, and the arbitrarily distortable Banach space $\mathbf{S}$ constructed by Schlumprecht. In recent joint work with Tomasz Kania it was shown that ``long'' sequence spaces of the form $c_0(\lambda)$, $\ell_{\infty}^c(\lambda)$ and $\ell_p(\lambda)$ (where $1 \leq p < \infty$) also enjoy this property. In the other direction, with the aid of a result of Kania--Koszmider--Laustsen we will show that for any separable, reflexive Banach space $X$ there is a Banach space $Y_X$ and a surjective algebra homomorphism $ \psi: \, \mathcal{B}(Y_X) \rightarrow \mathcal{B}(X)$ which is not injective. * 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 18: Chris Phillips, University of Oregon Thank you, and best regards, Bunyamin Sari

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Announcement of VOTCAM
by Bentuo Zheng (bzheng) 03 Sep '20

03 Sep '20

Hello, This is the 1st announcement for the 2020 Virginia Operator Theory and Complex Analysis Meeting (VOTCAM)<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…>, which will be held on Saturday, October 3rd. This year we have a great line-up of speakers from all around the world. The conference will take place entirely through Zoom. VOTCAM is an NSF-sponsored conference held annually since 1992 and features a mixture of speakers in Banach space theory, operator theory, operator algebras, and related areas. The talks are each 30 or 50 minutes and will take place between 8:00am and 5:00pm EDT. VOTCAM 2020 speakers: Lisa Orloff Clark - Victoria University of Wellingtonz<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> Noé de Rancourt - Kurt Godel Research Center<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> Joseph Eisner - University of Virginia<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> Adrian Ioana - University of California San Diego<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> Gideon Schechtman - Weizmann Institute of Sciences<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> Alan Sola - Stockholm University<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> This year, for the first time, we will also feature a discussion panel moderated by organizers David Sherman<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> and Kevin Beanland<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> with Masamichi Takesaki<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> and Bill Johnson<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…>. The theme of the panel is My Life in Mathematics. Special thanks to Stephen Hardy<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> for our truly excellent poster inspired by a 1959 Elvis album with a similar name. At this point, we're collecting names and email addresses to add to the Zoom registry. To be put on this list go here.<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…> VOTCAM is free and open to anyone, and you can request to register at any time. Again, in order to receive the Zoom link to attend please register here<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwordpress…>. Titles and abstracts of talks will be announced and posted soon. Please pass on this announcement to anyone that might be interested. The Organizing Committee: Kevin Beanland - Washington & Lee University Bill Ross - University of Richmond David Sherman - University of Virginia

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Banach spaces webinar on Friday Sep 4 by : Mary Angelica Tursi (The University of Illinois at Urbana–Champaign)
by Sari, Bunyamin 02 Sep '20

02 Sep '20

Dear all, The next Banach spaces webinar is on Friday September 4 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Mary Angelica Tursi (The University of Illinois at Urbana–Champaign) Title: A separable universal homogeneous Banach lattice Abstract: We prove the existence of a separable approximately ultra-homogeneous Banach lattice BL that is isometrically universal for separable Banach lattices. This is done by showing that the class of Banach lattices has the Amalgamation Property, and thus finitely generated Banach lattices form a metric Fraïssé class. Some additional results about the structural properties of BL are also proven. * 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 11: Bence Horváth, Czech Academy of Sciences Thank you, and best regards, Bunyamin Sari

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