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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
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 0212544
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [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] Albert Wilansky, Functional analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0170186

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Keywords: Extreme functional, uniform norm, function space, upper semicontinuous norm
Article copyright: © Copyright 1974 American Mathematical Society

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