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The Structure of C*-Convex Sets

Published online by Cambridge University Press:  20 November 2018

Phillip B. Morenz
Phillip B. Morenz*
Affiliation:
Department of Pure Mathematics, University of Waterloo Waterloo, Ontario N2L 3G1
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Abstract

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Compact C*-convex subsets of Mn correspond exactly to n-th matrix ranges of operators. The main result of this paper is to discover the “right” analog of linear extreme points, called structural elements, and then to prove a generalised Krein-Milman theorem for C*-convex subsets of Mn. The relationship between structural elements and an earlier attempted generalisation, called C*-extreme points, is examined, solving affirmatively a conjecture of Loebl and Paulsen [8]. An improved bound for a C* -convex version of the Caratheodory theorem for convex sets is also given.

Keywords

47A1215A3052A01
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 5 , 01 October 1994 , pp. 1007 - 1026
Copyright
Copyright © Canadian Mathematical Society 1994

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