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Denting points in Bochner $ L\sp p$-spaces


Authors: Bor-Luh Lin and Pei-Kee Lin
Journal: Proc. Amer. Math. Soc. 97 (1986), 629-633
MSC: Primary 46B20; Secondary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1986-0845978-X
MathSciNet review: 845978
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Abstract: A characterization of denting points in the unit balls of $ {L^p}(\mu ,X)$, $ 1 < p < \infty $, is given. This characterization is compared to similar known results concerning strongly extreme points and extreme points.


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

  • [F-G] K. Fan and I. Glicksberg, Some geometric properties of the spheres in normed linear space, Duke Math. J. 25 (1958), 553-568. MR 0098976 (20:5421)
  • [G1] P. Greim, Strongly exposed points in Bochner $ {L^p}$-spaces, Proc. Amer. Math. Soc. 88 (1983), 81-84. MR 691281 (84f:46044)
  • [G2] -, A note on strong extreme and strongly exposed points in Bochern $ {L^p}$-spaces, Proc. Amer. Math. Soc. 93 (1985), 65-66. MR 766528 (86g:46050)
  • [G3] -, An extremal vector-valued $ {L^p}$-function taking no extremal vectors as values, Proc. Amer. Math. Soc. 84 (1982), 65-68. MR 633279 (83c:46034)
  • [G4] -, An extension of J. A. Johnson's characterization of extremal vector-valued $ {L^p}$functions, preprint.
  • [J1] J. A. Johnson, Extreme measurable selections, Proc. Amer. Math. Soc. 44 (1974), 107-111. MR 0341068 (49:5818)
  • [J2] -, Strongly exposed points in $ {L^p}(\mu ,E)$, Rocky Mountain J. Math. 10 (1980), 517-519. MR 590215 (82a:41032)
  • [L-L] Bor-Luh Lin and Pei-kee Lin Property (H) in Lebesgue-Bochner function spaces, Proc. Amer. Math. Soc. 95 (1985), 581-584. MR 810168 (87a:46060)
  • [S1] M. A. Smith, Strongly extreme points in $ {L^p}(\mu ,X)$, Rocky Mountain J. Math. (to appear). MR 829190 (87d:46043)
  • [S2] -, Rotundity and extremity in $ {l^p}({X_i})$ and $ {L^p}(\mu ,X)$, preprint.
  • [Su] K. Sundaresan, Extreme points of the unit cell in Lebesgue-Bochner function spaces, Colloq. Math. 22 (1970), 111-119. MR 0276753 (43:2493)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0845978-X
Keywords: Bochner $ {L^p}$-space, denting point
Article copyright: © Copyright 1986 American Mathematical Society

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