Operator ideals associated with the Szlenk index

Philip A. H. Brooker

Operator ideals associated with the Szlenk index

Functional Analysis 2010-09-14 v2

Authors: 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.

Cite

@article{arxiv.1003.5706,
  title  = {Operator ideals associated with the Szlenk index},
  author = {Philip A. H. Brooker},
  journal= {arXiv preprint arXiv:1003.5706},
  year   = {2010}
}

Comments

This paper has been withdrawn by the author as it has been merged with arXiv:1003.5710

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