### Alejandra Cáceres: Tightness in Banach spaces with transfinite basis.

Data: sexta-feira, 7 de Maio de 2021, às 9h30.

Palestrante:
Alejandra Cáceres (IME-USP)

Título: Tightness in Banach spaces with transfinite basis.

Resumo:  The notion of tightness in Banach spaces with Schauder basis was defined and studied by Ferenczi and Rosendal (2007). In that work, they proved several dichotomies between different forms of tightness and their correspondent forms of minimality, as part of the program of classification of Banach spaces up to subspaces initiated by Gowers (2002). Later, Ferenczi and Godefroy (2012) characterized tightness in Banach spaces with Schauder basis using Baire category theory. We extend the ideas of Ferenczi and Godefroy and use Baire category theory to define tightness in Banach spaces with a transfinite basis over an infinite ordinal. We present some properties of tight spaces with a transfinite basis and study the relation between tight bases and the existence of separable minimal subspaces. Processo Fapesp Nº 2017/18976-5.

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