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A Banach–Stone theorem for spaces of weak* continuous functions

Published online by Cambridge University Press:  14 November 2011

Michael Cambern
Michael Cambern
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A
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Synopsis

If X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 203 - 206
Copyright
Copyright © Royal Society of Edinburgh 1985

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