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Extreme functionals on an upper semicontinuous function space


Authors: F. Cunningham and Nina M. Roy
Journal: Proc. Amer. Math. Soc. 42 (1974), 461-465
MSC: Primary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1974-0328579-3
MathSciNet review: 0328579
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Abstract: A representation theorem is given for the extreme points of the dual ball of a vector valued function space X with upper semicontinuous norm defined on a compact Hausdorff space $ \Omega $. This generalizes the Arens-Kelley theorem which is the case $ X = C(\Omega )$.


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

  • [1] F. Cunningham, Jr., M-structure in Banach spaces, Proc. Cambridge Philos. Soc. 63 (1967), 613-629. MR 35 #3415. MR 0212544 (35:3415)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] W. J. Ströbele, On the representation of the extremal functionals on $ {C_0}(T,X)$, Notices Amer. Math. Soc. 19 (1972), A-443. Abstract 72T-B119.
  • [4] A. Wilansky, Functional analysis, Blaisdell, New York, 1964. MR 30 #425. MR 0170186 (30:425)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328579-3
Keywords: Extreme functional, uniform norm, function space, upper semicontinuous norm
Article copyright: © Copyright 1974 American Mathematical Society

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