Operator ideals associated with the Szlenk index

Abstract

For $\alpha$ an ordinal, we investigate the class ${\mathcal{SZ}}_{\alpha }$ consisting of all operators whose Szlenk index is an ordinal not exceeding ${\omega }^{\alpha }$. Our main result is that ${\mathcal{SZ}}_{\alpha }$ is a closed, injective, surjective operator ideal for each $\alpha$. We also study the relationship between the classes ${\mathcal{SZ}}_{\alpha }$ and several well-known closed operator ideals.

This paper has been withdrawn by the author as it has been merged with arXiv:1003.5710

References in corpus (1)

• Direct sums and the Szlenk index