Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js
Previous issue ·  Next issue ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Journal of Operator Theory

Volume 68, Issue 2, Fall 2012  pp. 405-442.

Asplund operators and the Szlenk index

Authors 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.


Contents    Full-Text PDF