### Manuel González: Subprojective and superprojective Banach spaces

Data: quarta-feira, 15 de abril de 2015, às 10h

Sala: 266-A

Palestrante: Manuel González, Universidad de Cantabria

Título: Subprojective and superprojective Banach spaces

Resumo: A Banach space $X$ is called subprojective if each of its infinite dimensional (closed) subspaces contains an infinite dimensional subspace complemented in $X$, and it is called superprojective if each of its infinite codimensional subspaces is contained in an infinite codimensional subspace complemented in $X$.

The space $L_p(0,1)$ is subprojective iff $2\leq p<\infty$, and it is superprojective iff $1<p\leq 2$. These two notions were introduced by Whitley in 1964 to study the adjoints of strictly singular and strictly cosingular operators, respectively. More recently they were applied to obtain some positive answers to the perturbation classes problem for semi-Fredholm operators.

In this talk we describe the basic properties and examples of these two classes of Banach spaces, we present some recent results of stability under vector sums and tensor products that provide new examples, and we point out some open problems.