The Complete Continuity Property and Finite Dimensional Decompositions
Abstract
A Banach space $\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\X$ 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1993
 arXiv:
 arXiv:math/9302204
 Bibcode:
 1993math......2204G
 Keywords:

 Mathematics  Functional Analysis;
 46B