We investigate first Baire functionals on the dual ball of a separable Banach space X which are pointwise limit of a sequence of X whose closed span does not contain any copy of \ell_1 (or has separable dual). We propose an example of a C(K) space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.

On certain classes of first Baire functionals.

Puglisi, D.
2024-01-01

Abstract

We investigate first Baire functionals on the dual ball of a separable Banach space X which are pointwise limit of a sequence of X whose closed span does not contain any copy of \ell_1 (or has separable dual). We propose an example of a C(K) space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.
2024
First Baire functions, Analytic and coanalytic sets
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/619074
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