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Asymptotic-norming and Mazur intersection properties in Bochner function spaces

Published online by Cambridge University Press:  17 April 2009

Zhibao Hu  and
Bor-Luh Lin
Zhibao Hu
Affiliation:
Department of Mathematics and Statistics, Miami University Oxford, Ohio 45056-1641, United States of America
Bor-Luh Lin
Affiliation:
Department of Mathematics, University of Iowa Iowa City, Iowa 52242, United States of America
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A Banach space X has the asymptotic-norming property if and only if the Lebesgue-Bochner function space Lp (μ, X) has the asumptotic-norming property for p with 1 < p < ∞. It follows that a Banach space X is Hahn-Banach smooth if and only if Lp (μ, X) is Hahn-Banach smooth for p with 1 < p < ∞. We also show that for p with 1 < p < ∞, (1) if X has the compact Mazur intersection property then so does Lp(μ, X); (2) if the measure μ is not purely atomic, then the space Lp(μ, X) has the Mazur intersection property if and only if X is an Asplund space and has the Mazur intersection property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 177 - 186
Copyright
Copyright © Australian Mathematical Society 1993

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