Minimality properties of Tsirelson type spaces
Functional Analysis
2007-05-23 v1
Abstract
In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a further block (y_k) of (x_k) such that (y_k) is equivalent to a subsequence of (e_k). Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal and connections with Bourgain's \ell^{1}-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.
Keywords
Cite
@article{arxiv.math/0702210,
title = {Minimality properties of Tsirelson type spaces},
author = {Denka Kutzarova and Denny Leung and Antonis Manoussakis and Wee Kee Tang},
journal= {arXiv preprint arXiv:math/0702210},
year = {2007}
}