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Tuesday, 18 November 2025 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Michal Doucha, Institute of Mathematics, Czech Academy of Sciences<br />
Title: Invariant strictly convex renormings
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Abstract <br />
<p>I will present my observations concerning a problem posed by Mikael de la Salle several years ago: Given a topological group acting continuously by linear isometries on some Banach space, under which conditions – on the Banach space, the group, and the action – does there exist an equivalent strictly convex norm on the Banach space that is invariant with respect to the action?</p><p>Based on the expected audience, I will most likely present the following ‘quasi-dichotomy’: Denoting by K the Cantor space, (i) for a generic action of a countable locally finite group on C(K) by linear isometries, there is an equivalent and invariant strictly convex norm on C(K); (ii) for a generic action of a countable group containing the free group on two generators on C(K) by positive linear isometries, there is no equivalent and invariant strictly convex norm on C(K).</p><p><br></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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