Journal of Operator Theory
Volume 68, Issue 2, Fall 2012 pp. 405-442.
Asplund operators and the Szlenk indexAuthors: Philip A.H. Brooker
Author institution: Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia
Summary: For α an ordinal, we investigate the class \szlenkopα consisting of all operators whose Szlenk index is an ordinal not exceeding ωα. We show that each class \szlenkopα is a closed operator ideal and study various operator ideal properties for these classes. The relationship between the classes \szlenkopα 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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