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.
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Mirmina, J., Puglisi, D. On certain classes of first Baire functionals. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01464-5
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DOI: https://doi.org/10.1007/s10474-024-01464-5