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.File in questo prodotto:
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