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Strongly exposed points in Lebesgue-Bochner function spaces


Authors: Zhibao Hu and Bor-Luh Lin
Journal: Proc. Amer. Math. Soc. 120 (1994), 1159-1165
MSC: Primary 46E40; Secondary 46B20
MathSciNet review: 1176069
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Abstract: It is a result of Peter Greim that if $ f$ is a strongly exposed point of the unit ball of Lebesgue-Bochner function space $ {L^p}(\mu ,X),\;1 < p < \infty $, then $ f$ is a unit vector and $ f(t)/\vert\vert f(t)\vert\vert$ is a strongly exposed point of the unit ball of $ X$ for almost all $ t$ in the support of $ f$. We prove that the converse is also true.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1176069-3
Keywords: Lebesgue-Bochner function space, strongly exposed point, slice
Article copyright: © Copyright 1994 American Mathematical Society