No abstract

For α an ordinal, we investigate the class SZ α consisting of all operators whose Szlenk index is an ordinal not exceeding ω α . We show that each class SZ α is a closed operator ideal and study various operator ideal properties for these classes. The relationship between the classes SZ α and several wellknown closed operator ideals is investigated and quantitative factorization results in terms of the Szlenk index are obtained for the class of Asplund operators.