The Complete Continuity Property and Finite Dimensional Decompositions
Functional Analysis
2008-02-03 v1
Abstract
A Banach space has the complete continuity property (CCP) if each bounded linear operator from into is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP (resp., failing the CCP and failing cotype) has a subspace with a finite dimensional decomposition (resp., basis) which fails the CCP.
Cite
@article{arxiv.math/9302204,
title = {The Complete Continuity Property and Finite Dimensional Decompositions},
author = {Maria Girardi and William B. Johnson},
journal= {arXiv preprint arXiv:math/9302204},
year = {2008}
}