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Fréchet differentiable points in Bochner function spaces $ L\sb p(\mu,X)$

Authors: Jian Hua Wang and Chao Xun Nan
Journal: Proc. Amer. Math. Soc. 104 (1988), 76-78
MSC: Primary 46E40; Secondary 46B20, 46E30
MathSciNet review: 958046
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Abstract: In this paper, a characterization of Fréchet differentiable points of $ {L_p}(\mu ,X),1 < p < \infty $, is given: $ f \in {L_p}(\mu ,X),f \ne 0$ is a point of Fréchet differentiability of the norm if and only if the values $ f(t)$ are such almost everywhere in the support of $ f$.

References [Enhancements On Off] (What's this?)

  • [1] P. Greim, A note on strong extreme and strongly exposed point in Bochner $ {L^p}$-spaces, Proc. Amer. Math. Soc. 93 (1985), 65-66. MR 766528 (86g:46050)
  • [2] I. E. Leonard and K. Sundaresan, Geometry of Lebesgue-Bochner function spaces--smoothness, Trans. Amer. Math. Soc. 198 (1974), 229-251. MR 0367652 (51:3894)
  • [3] J. Diestel, Geometry of Banach spaces selected topics, Lecture Notes in Math., vol. 485, Springer-Verlag, Berlin and New York, 1975. MR 0461094 (57:1079)

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Keywords: Fréchet differentiable point, strongly exposed point, Bochner function space
Article copyright: © Copyright 1988 American Mathematical Society

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