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Distances between convex subsets of state spaces

Published online by Cambridge University Press:  17 April 2009

A.J. Ellis
A.J. Ellis
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National Univerity, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

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Let L be a closed linear space of continuous real-valued functions, containing constants, on a compact Hausdorff space Ω. This paper gives some new criteria for a closed subset E of Ω to be an L-interpolation set, or more generally for L|E to be uniformly closed or simplicial, in terms of distances between certain compact convex subsets of the state space of L. These criteria involve the facial structure of the state space and hence are of a geometric nature. The results sharpen some standard results of Glicksberg.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 109 - 117
Copyright
Copyright © Australian Mathematical Society 1985

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