  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.

Functional Analysis