Banach Spaces Of The Type Of Tsirelson
Functional Analysis
2016-09-06 v1
Abstract
To any pair ( M , theta ) where M is a family of finite subsets of N compact in the pointwise topology, and 0<theta < 1 , we associate a Tsirelson-type Banach space T_M^theta . It is shown that if the Cantor-Bendixson index of M is greater than n and theta >{1/n} then T_M^theta is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than omega then T_M^theta does not contain any l^p, while if the Cantor-Bendixson index of M is finite thenT_M^theta contains some l^p or c_o . In particular, if M ={ A subset N : |A| leq n } and {1/n}<theta <1 then T_M^theta is isomorphic to some l^p .
Keywords
Cite
@article{arxiv.math/9207206,
title = {Banach Spaces Of The Type Of Tsirelson},
author = {Spiros A. Argyros and Irene Deliyanni},
journal= {arXiv preprint arXiv:math/9207206},
year = {2016}
}