Extreme functionals on an upper semicontinuous function space
HTML articles powered by AMS MathViewer
- by F. Cunningham and Nina M. Roy PDF
- Proc. Amer. Math. Soc. 42 (1974), 461-465 Request permission
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
- F. Cunningham Jr., $M$-structure in Banach spaces, Proc. Cambridge Philos. Soc. 63 (1967), 613–629. MR 212544, DOI 10.1017/s0305004100041591
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523 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.
- Albert Wilansky, Functional analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0170186
Additional Information
- © Copyright 1974 American Mathematical Society
- 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