November 2020 - Banach - mathdept.okstate.edu

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 Moreover, using an unpublished argument by Johnson, and showing a combinatorial result on higher order Schreier families, we also deduce that $\mathcal L(T^p_\xi)$, for $\xi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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