### Alejandra Cáceres Rigo: About tight Banach spaces

Data: segunda-feira, 4 de novembro de 2019, às 11h30.

Sala: B143

Palestrante:
Alejandra Cáceres Rigo (IME-USP)

Resumo:  A Banach space $Y$ is tight in a Banach space $X$ with Schauder
basis $(e_n)_n$, if there is a sequence of successive non-empty intervals
$I_0 < I_1< I_2< ...$ of $\omega$ such that if $Y$ embeds into
$\overline{span}[e_n : n \in u]$, then $u \in 2^\omega$ intersects all but
finitely many intervals $I_i$. $(e_n)_n$ is a tight basis for $X$ if $Y$ is
tight in $X$, for all Banach space $Y$. This notion and other types of
tightness were presented by V. Ferenczi and Ch. Rosendal in order to obtain
further dichotomies which improve the Gowers' program of classifying Banach
spaces. In this talk some basic results involving tightness will be studied
and some recent problems will be presented.