The Szlenk index and local l_1-indices
Functional Analysis
2007-05-23 v1
Abstract
We introduce two new local l_1-indices of the same type as the Bourgain l_1 index; the l_1^+-index and the l_1^+-weakly null index. We show that the l_1^+-weakly null index of a Banach space X is the same as the Szlenk index of X, provided X does not contain l_1. The l_1^+-weakly null index has the same form as the Bourgain l_1 index: if it is countable it must take values omega^alpha for some alpha<omega_1. The different l_1-indices are closely related and so knowing the Szlenk index of a Banach space helps us calculate its local l_1-index, via the l_1^+-weakly null index. We show that I(C(omega^{omega^alpha}))=omega^{1+alpha+1}.
Cite
@article{arxiv.math/0009250,
title = {The Szlenk index and local l_1-indices},
author = {Dale Alspach and Robert Judd and Edward Odell},
journal= {arXiv preprint arXiv:math/0009250},
year = {2007}
}
Comments
LaTeX2e, 41 pages, to appear in Positivity