The Complete Continuity Property and Finite Dimensional Decompositions

@article{Girardi1993TheCC,
  title={The Complete Continuity Property and Finite Dimensional Decompositions},
  author={Maria Girardi and W. Johnson},
  journal={arXiv: Functional Analysis},
  year={1993},
  pages={207-214}
}
  • Maria Girardi, W. Johnson
  • Published 1993
  • Mathematics
  • arXiv: Functional Analysis
  • 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.