<!DOCTYPE html>
<html>
<head>
<title>Set Theory and Analysis</title>
</head>
<body>
<p>
Tuesday, 7 January 2025 - 10:00 to 11:30 <br />
Place: IM, konírna
</p>
<p>
Speaker: Zdeněk Silber, IM CAS<br />
Title: Weak compactness in Lipschitz-free spaces over superreflexive spaces
</p>
<p class="ql-ed">
Abstract <br />
<p>Inspired by the famous result of Rosenthal, that a subspace of L_1 that does not contain l_1 is superreflexive, we define property (R) of Banach spaces -- a Banach space has (R) if and only if every weakly precompact (that is bounded not containing a sequence equivalent to the l_1 basis) subset is relatively super weakly compact (this is a localisation of superreflexivity in the same way as relative weak compactness is a localisation of reflexivity). We investigate property (R) and finally show that Lipschitz-free spaces over superreflexive spaces have property (R) proving some new non-embeddability results. The proof is based on the proof of weak sequential completeness of such spaces by Kochanek and Pernecká and an appropriate version of compact reduction in the spirit of Aliaga, Nous, Petitjean and Procházka.</p>
</p>
<p>
For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
</p>
<p>
Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
</p>
</body>
</html>