Fréchet differentiable points in Bochner function spaces $L_ p(\mu ,X)$
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- by Jian Hua Wang and Chao Xun Nan PDF
- Proc. Amer. Math. Soc. 104 (1988), 76-78 Request permission
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
- Peter Greim, A note on strong extreme and strongly exposed points in Bochner $L^p$-spaces, Proc. Amer. Math. Soc. 93 (1985), no. 1, 65–66. MR 766528, DOI 10.1090/S0002-9939-1985-0766528-1
- I. E. Leonard and K. Sundaresan, Geometry of Lebesgue-Bochner function spaces—smoothness, Trans. Amer. Math. Soc. 198 (1974), 229–251. MR 367652, DOI 10.1090/S0002-9947-1974-0367652-5
- Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094, DOI 10.1007/BFb0082079
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 76-78
- MSC: Primary 46E40; Secondary 46B20, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958046-5
- MathSciNet review: 958046