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Remarks on James's distortion theorems II

Published online by Cambridge University Press:  17 April 2009

Patrick N. Dowling ,
Narcisse Randrianantoanina  and
Barry Turett
Patrick N. Dowling
Affiliation:
Department of Mathematics and StatisticsMiami UniversityOxford, OH 45056, United States of America e-mail: [email protected]
Narcisse Randrianantoanina
Affiliation:
Department of Mathematics and StatisticsMiami UniversityOxford, OH 45056, United States of America e-mail: [email protected]
Barry Turett
Affiliation:
Department of Mathematics and StatisticsOakland UniversityRochester, MI 48309, United States of America e-mail: [email protected]
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Abstract

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If a Banach space X contains a complemented subspace isomorphic to ℓ1 and if ε > 0, then there exists a subspace Y of X and a projection P from X onto Y such that Y is (1 + ε)-isometric to ℓ1 and ∥P∥ ≤ 1 + ε. A stronger result for c0 is proved for Banach spaces whose dual unit ball is weak sequentially compact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 515 - 522
Copyright
Copyright © Australian Mathematical Society 1999

References

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