Asplund operators and the Szlenk index

Details Asplund operators and the Szlenk index Asplund operators and the Szlenk index

2010-03-30

arxiv.org/abs/1003.5710v4

Mathematics

Functional Analysis

This version corrects several typos and implements changes as per the referees suggestions, including removal of Proposition 2

Scientific paper

For $\alpha$ an ordinal, we investigate the class $\mathscr{SZ}_\alpha$ consisting of all operators whose Szlenk index is an ordinal not exceeding $\omega^\alpha$. We show that each class $\mathscr{SZ}_\alpha$ is a closed operator ideal and study various operator ideal properties for these classes. The relationship between the classes $\mathscr{SZ}_\alpha$ and several well-known closed operator ideals is investigated and quantitative factorization results in terms of the Szlenk index are obtained for the class of Asplund operators.

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