The Bourgain Subset of Baire-1 Functions and Descriptive Set Theory – Jeremy Mirmina (Università di Pisa)


Aula Seminari


Given a Banach space $X$, a functional in $X^{**}$ is said to be Baire-1 if it is the pointwise limit of a bounded sequence of X. The study of the properties of the set of Baire-1 functions, denoted as $B_1$, provides us with valuable information about the structure and the geometry of the space. In this talk, we investigate the properties of the Bourgain set $B_1^1$, which is the set of Baire-1 functions that are pointwise limits of sequences whose linear span does not contain $I_1$. In particular, we study the family of separable Banach spaces for which the inclusion $B_1^1\subset B_1$ is strict from the Descriptive Set Theory point of view.

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