This is an announcement for the paper "Factorisation properties and space ideals associated with the Szlenk index" by Philip A. H. Brooker.
Abstract: For $\alpha$ an ordinal, we study factorisation properties of the operator ideal $\mathscr{SZ}_\alpha$ of $\alpha$-Szlenk operators. We obtain quantitative factorisation results for Asplund operators in terms of the Szlenk index and a partial characterisation of those ordinals $\alpha$ for which $\mathscr{SZ}_\alpha$ has the factorisation property. Our investigations lead to the study of a class of space ideals defined in terms of a renorming property involving the Szlenk index.
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/1003.5710
or