Operator ideals associated with the Szlenk index

Details Operator ideals associated with the Szlenk index Operator ideals associated with the Szlenk index

2010-03-30

arxiv.org/abs/1003.5706v2

Mathematics

Functional Analysis

This paper has been withdrawn by the author as it has been merged with arXiv:1003.5710

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 $\omega^\alpha$. 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.

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