Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Property $ (H)$ in Lebesgue-Bochner function spaces

Authors: Bor-Luh Lin and Pei-Kee Lin
Journal: Proc. Amer. Math. Soc. 95 (1985), 581-584
MSC: Primary 46E40; Secondary 46B20
MathSciNet review: 810168
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Abstract: We prove that if a Banach space $ X$ has the property (HR) and if $ {l_1}$ is not isomorphic to a subspace of $ X$, then every point on the unit sphere of $ X$ is a denting point of the closed unit ball. We also prove that if $ X$ has the above property, then $ {L^p}\left( {\mu ,X} \right)$, $ 1 < p < \infty $, has the property (H).

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Keywords: Property (H), Lebesgue-Bochner function spaces
Article copyright: © Copyright 1985 American Mathematical Society