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Denseness of norm-attaining operators into strictly convex spaces

Published online by Cambridge University Press:  14 November 2011

M. D. Acosta
M. D. Acosta
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain (dacosta@goliat.ugr.es)
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Extract

We show that no infinite-dimensional Banach space provided with a strictly convex norm satisfies Lindenstrauss's property B. This is a generalization of previous results by Lindenstrauss for rotund spaces isomorphic to C0 and by Gowers for ℓp (1 < p < ∞). Also, there is an appropriate complex version of the announced result that works for all the C-strictly convex spaces. As a consequence, the Hardy space H1, any infinite-dimensional complex L1(μ), and, in general, any infinite-dimensional predual of a von Neumann algebra lacks Lindenstrauss's property B.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 6 , 1999 , pp. 1107 - 1114
Copyright
Copyright © Royal Society of Edinburgh 1999

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