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The Complete Continuity Property and Finite Dimensional Decompositions

Maria Girardi·William B. Johnson
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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.

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Maria Girardi, William B. Johnson. 1993-02-02. The Complete Continuity Property and Finite Dimensional Decompositions. https://arxiv.org/abs/math/9302204

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