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Tuesday, 17 December 2024 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Noé De Rancourt, Université de Lille<br />
Title: Guarded Fraïssé Banach spaces
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Abstract <br />
<p>In a recent paper, Cúth, Doležal, Doucha and Kurka developed several Polish codings of separable Banach spaces and showed that in each of them, the Gurarij space and the spaces Lp[0, 1] have G_\delta isometry classes. They asked if those spaces are the only ones to satisfy this property. In another recent paper, Ferenczi, Lopez-Abad, Mbombo and Todorcevic developed an (approximate) Fraïssé theory for separable Banach spaces and showed that the Gurarij space and (most of) the spaces Lp[0, 1] were Fraïssé limits. They asked if those spaces are the only ones to satisfy this property.</p><p><br></p><p>In this talk, I'll present a common work with Marek Cúth and Michal Doucha where we unified those two problems. More precisely, we developed a weak Fraïssé theory for Banach spaces (using the adjective "guarded" rather than "weak" to avoid conflicts of terminology) and proved that a separable Banach space is guarded Fraïssé iff it has a G_\delta isometry class. Combining this result with results from model theory of Banach spaces, we were able to prove that many of the spaces Lp([0, 1], Lq[0,1]) have G_\delta isometry classes, thus answering Cúth-Doležal-Doucha-Kurka's question.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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