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arXiv · 1003.5706

Operator ideals associated with the Szlenk index

Philip A. H. Brooker
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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.

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Philip A. H. Brooker. 2010-03-30. Operator ideals associated with the Szlenk index. https://arxiv.org/abs/1003.5706

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