Maria Girardi, William B. Johnson
Published 1993-02-02Version 1
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.
Smooth norms and approximation in Banach spaces of the type C(K)
Vector-valued Walsh-Paley martingales and geometry of Banach spaces
Embedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces
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