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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 L 1 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

Information

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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