October 2020 - Banach - mathdept.okstate.edu

Banach spaces webinar on Friday October 30 by Victor Reis (University of Washington)
by Sari, Bunyamin 26 Oct '20

26 Oct '20

Dear all, The next Banach spaces webinar is on Friday October 30 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Victor Reis, University of Washington Title: An Elementary Exposition of Pisier's Inequality Abstract: Pisier's inequality is central in the study of normed spaces and has important applications in geometry. We provide an elementary proof of this inequality by constructing an explicit linear proxy function for a suitable probability distribution, thus avoiding some non-constructive steps in previous proofs. We also show a simplification of Bourgain's construction which is sufficient to give a nearly tight matching lower bound. 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 Oct 23 by Przemyslaw Wojtaszczyk (Polish Academy)
by Sari, Bunyamin 20 Oct '20

20 Oct '20

Dear all, The next Banach spaces webinar is on Friday October 23 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Przemyslaw Wojtaszczyk, Institut of Mathematics Polish Academy of Sciences Title: Quasi-greedy bases in $p$-Banach spaces Abstract: This talk is based on the paper F. Albiac, J.L. Ansorena and P.W. \emph{On certain subspaces of $\ell_p$ for $0<p\le 1$ and their applications to conditional quasi-greedy bases in $p$-Banach spaces} Mathematische Annalen--available on line. We construct new quasi-greedy bases in $\ell_p$ and in the kernels of certain quotient maps from $\ell_p $ onto $L_p$, $0<p\leq 1$ and study its properties. We note that all the kernels we study are isomorphic; we denote this space as ${\mathfrak l }_p$ . We show that there is continuum of non-equivalent quasi-greedy bases in $\ell_p$ and ${\mathfrak l }_p$ and we study the conditionality of those bases. 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 Oct 16 by Mitchell Taylor (UC Berkeley)
by Sari, Bunyamin 13 Oct '20

13 Oct '20

Dear all, The next Banach spaces webinar is on Friday October 16 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Mitchell Taylor, UC Berkeley Title: Free Banach lattices: subspace structure and basic sequences Abstract: Given a Banach space E, one can associate a Banach lattice FBL[E] with the property that every bounded operator from E to a Banach lattice X extends uniquely to a lattice homomorphism from FBL[E] into X. We will discuss the structure of FBL[E], and give complete answers to questions like ``when does an embedding of E into F induce a lattice embedding of FBL[E] into FBL[F]?" This is joint work with Timur Oikhberg, Pedro Tradacete and Vladimir Troitsky. 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 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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