Richard Smith

will speak on

A topological characterization of dual strict convexity in Asplund spaces II

Time: 4:00PM
Date: Tue 30th April 2019
Location: Seminar Room SCN 1.25 [map]

Abstract: In 1975 Lindenstrauss asked whether it is possible to characterize Banach spaces $X$ that admit an equivalent strictly convex norm, in terms of other linear or topological properties of $X$. We provide a partial answer to this problem in the case of dual spaces, by showing that if $X$ is an Asplund space, then it admits an equivalent norm having a strictly convex dual norm if and only if the dual unit sphere $S_{X^*}$ (equivalently $X^*$), endowed with the $w^*$-topology, possesses a certain topological property. It follows that this ostensibly geometric property of the space can in fact be characterised in purely non-linear, topological terms. In the second of two talks we will sketch the proof of this characterization.

(This talk is part of the Analysis series.)

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