Asplund operators and the Szlenk index

Philip A. H. Brooker

Asplund operators and the Szlenk index

Functional Analysis 2011-09-19 v4

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 $\omega^\alpha$ . 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.

Keywords

operator theory

Cite

@article{arxiv.1003.5710,
  title  = {Asplund operators and the Szlenk index},
  author = {Philip A. H. Brooker},
  journal= {arXiv preprint arXiv:1003.5710},
  year   = {2011}
}

Comments

This version corrects several typos and implements changes as per the referees suggestions, including removal of Proposition 2.11 of the previous version. This version shall appear in Journal of Operator Theory

Asplund operators and the Szlenk index

Abstract

Keywords

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