This is an announcement for the paper "Operator ideals associated with the Szlenk index" by Philip A. H. Brooker.

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

Archive classification: math.FA

Submitted from: philip.brooker@anu.edu.au

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1003.5706

or

http://arXiv.org/abs/1003.5706