The Complete Continuity Property and Finite Dimensional Decompositions
نویسندگان
چکیده
A Banach space X has the complete continuity property (CCP) if each bounded linear operator from L1 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 has a subspace with a nite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such as fails cotype or is a lattice), then the decomposition may be strengthened to a bases.
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