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Banach spaces webinar on Friday 12/11 by José Luis Ansorena (Universidad de La Rioja)
by Sari, Bunyamin 07 Dec '20

07 Dec '20

Dear all, The next Banach spaces webinar is on Friday December 11 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: José Luis Ansorena (Universidad de La Rioja) Title: On the permutative equivalence of squares of unconditional bases Abstract: We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty two year-old question raised by Casazza and Kalton in [Uniqueness of unconditional bases in Banach spaces, Israel J. Math. 103 (1998), 141--175]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. This is joint work with Fernando Albiac. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Best regards, Bunyamin

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post-doc position at the University of São Paulo
by valentin ferenczi 02 Dec '20

02 Dec '20

Dear colleague, We would like to announce a post-doctoral position in the Department of Mathematics of the University of São Paulo (Brazil) within the scope of Geometry of Banach spaces. This position is for a period of 12 to 24 months and must end on January 31th 2023 at the latest. The initial date of the activities is negotiable, but preferably between February and September 2021, and the deadline to apply is January 15th, 2021. The position is available as part of the FAPESP Thematic Project "Geometry of Banach spaces": https://geometryofbanachspaces.wordpress.com/ The position has no teaching duties and includes a monthly stipend which is, as of December 1, 2020 of BRL 7373,10 (tax free). It also includes partial support for travel and the first expenses upon arrival, as well as Research Contigency Funds equivalent to 15% of the fellowship. All relevant information may be found at https://geometryofbanachspaces.wordpress.com/postdoc-position-open/ Don't hesitate to contact me for additional information. All the best, Valentin Ferenczi.

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Banach spaces webinar on Friday 12/4 by Thomas Schlumprecht (Texas A&M)
by Sari, Bunyamin 30 Nov '20

30 Nov '20

Dear all, The next Banach spaces webinar is on Friday December 4 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Thomas Schlumprecht (Texas A&M) Title: Banach Spaces which admit lots of closed Operator Ideals Abstract. We present general conditions which imply that for a Banach space $X$, which has an unconditional basis, the space of bounded linear operators $ L(X)$ has $2^{\frak c}$ ``small'' closed ideals (ideals which are generated by finitely strictly singular operators). The class of spaces which satisfy these conditions include:\\ $\ell_p\oplus \ell_q$, $1<p<q<\infty$,\\ $\ell_1\oplus \ell_p$, $c_0\oplus \ell_p$, $\ell_\infty\oplus \ell_p$, $1<p<\infty$,\\ $T^p_\xi\oplus T^q_\xi$, $1< p<q<\infty$, $T^p_\xi$ being the $p$-convexification of the Tsireson space of order $\xi<\omega_1$,\\ $S^p_\xi$, $1\le p<\infty$, $S^p_\xi$ being the $p$-convexification of the Schreier space of order $\xi<\omega_1$, Using arguments by Beanland, Kania, Laustsen, as well as Gasparis and Leung we show that $\mathcal L(S^p_\xi)$, and $\mathcal L(T^p_\xi)$, for $\xi<\omega$, has $2^{\frak c}$ ``large'' closed ideals (ideals generated by projections on subspaces which are spanned by subsequences of the basis). Moreover, using an unpublished argument by Johnson, and showing a combinatorial result on higher order Schreier families, we also deduce that $\mathcal L(T^p_\xi)$, for $\xi<\omega_1$, has $2^{\frak c}$ large closed ideals. Part of this talk is on joint work with Dan Freeman and \'Andras Zsak. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Best regards, Bunyamin Bunyamin Sari

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Banach spaces webinar on Friday 11/27 by Antonis Manoussakis (Technical University of Crete)
by Sari, Bunyamin 23 Nov '20

23 Nov '20

Dear all, The next Banach spaces webinar is on Friday November 27 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Antonis Manoussakis (Technical University of Crete) Title: A variant of the James tree space Abstract. We will discuss the first part of a work in progress, leading to the construction of an $\ell_{2}$-saturated $d_{2}-$H.I. space. The class of $d_{2}$-H.I. Banach spaces is defined in a recent work of W.Cuellar Carrera, N. de Rancourt and V. Ferenczi where also the problem of the existence of $\ell_{2}$-saturated $d_{2}$-H.I space was posed. In this talk we will present a classical analogue of this space, which is a reflexive space with an unconditional basis, based on the James tree construction. We will discuss its properties and its connection to the desired $d_{2}$-H.I space. Joint work with Spiros Argyros and Pavlos Motakis For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Happy Thanksgiving! Bunyamin Sari

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Banach spaces webinar on Friday 11/20 by Jamal Kawach (University of Toronto)
by Sari, Bunyamin 17 Nov '20

17 Nov '20

Dear all, The next Banach spaces webinar is on Friday November 20 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Jamal Kawach, University of Toronto Title: Approximate Ramsey properties of Fréchet spaces Abstract. In this talk we will consider various Fraïssé-theoretic aspects of Fréchet spaces, which we view as topological vector spaces equipped with a compatible sequence of semi-norms. We will show that certain classes of finite-dimensional Fréchet spaces satisfy a version of the approximate Ramsey property for Banach spaces. We will then see how this property is related to the topological dynamics of the isometry groups of approximately ultrahomogeneous Fréchet spaces. This talk contains joint work in progress with Jordi López-Abad. 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 11/13 by : Eva Pernecká (Czech Technical University in Prague)
by Sari, Bunyamin 10 Nov '20

10 Nov '20

Dear all, The next Banach spaces webinar is on Friday November 13 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Eva Pernecká, Czech Technical University in Prague Title: Lipschitz free spaces and their biduals Abstract: We will study continuous linear functionals on Lipschitz spaces with special focus on those belonging to canonical preduals, the Lipschitz free spaces. We will show that in order to verify weak$^*$ continuity of a functional, it suffices to do so for bounded monotone nets of Lipschitz functions. Then, after introducing a notion of support for the functionals, we will discuss their relation to measures. In particular, we will identify the functionals induced by measures as those functionals that admit a Jordan-like decomposition into a positive and a negative part. The talk will be based on joint work with Ramón J. Aliaga. 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 November 6 by Dirk Werner (Freie Universität Berlin)
by Sari, Bunyamin 04 Nov '20

04 Nov '20

Dear all, The next Banach spaces webinar is on Friday November 6 at 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Dirk Werner, Freie Universität Berlin Title: Vector space structure in the set of norm attaining functionals Abstract: The talk discusses the existence (or non-existence) of vector subspaces of the dual space consisting entirely of norm attaining functionals. 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 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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