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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810168-2
PII: S 0002-9939(1985)0810168-2
Keywords: Property (H), Lebesgue-Bochner function spaces
Article copyright: © Copyright 1985 American Mathematical Society