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The Complete Continuity Property and Finite Dimensional Decompositions

Published online by Cambridge University Press:  20 November 2018

Maria Girardi  and
William B. Johnson
Maria Girardi
Affiliation:
University of South Carolina, Department of Mathematics, Columbia, South Carolina 29208 U.S.A. e-mail:girardi@math.scarolina.edu
William B. Johnson
Affiliation:
Texas A&M University Department of Mathematics, College Station, Texas 77843, U.S.A. e-mail:WBJ7835@venus.tamu.edu
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Abstract

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A Banach space has the complete continuity property (CCP) if each bounded linear operator from L1 into 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 finite 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 basis.

Keywords

46B2246B2046B2846G99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 207 - 214
Copyright
Copyright © Canadian Mathematical Society 1995

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