When is the Szlenk derivation of a dual unit ball another ball?

Prelegent(ci)

Tomasz Kochanek

Afiliacja

UW

Język referatu

angielski

Termin

4 grudnia 2024 16:15

Pokój

p. 5050

Tytuł w języku polskim

When is the Szlenk derivation of a dual unit ball another ball?

Seminarium

Seminarium „Topologia i teoria mnogości”

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The Szlenk derivation of the dual unit ball of a Banach space is an analogue of the Cantor-Bendixson derivative, and the main ingredient in the definition of Szlenk index, a classical ordinal index with many applications in Banach space theory. In this talk, we are interested in characterizing the situation where all ɛ-Szlenk derivations of the unit ball of X* are balls. We prove that this is the case if X is separable and satisfies Kalton's property (M*). However, the converse implication is not true, as is witnessed by the dual of Baernstein's space which fails property (M*), but for which all ɛ-Szlenk derivation of the dual unit ball are balls with the same radius as for the separable Hilbert space. We will also derive estimates for the radii of enveloping balls of ɛ-Szlenk derivations for Tsirelson's space and the dual of Schlumprecht's space.

This is a joint work with Marek Miarka; preprint available at: https://arxiv.org/abs/2409.05516

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