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Extensions of states of C* -algebras, II

Published online by Cambridge University Press:  14 November 2011

R. J. Archbold ,
J. W. Bunce  and
K. D. Gregson
R. J. Archbold
Affiliation:
Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY
J. W. Bunce
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.
K. D. Gregson
Affiliation:
Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY
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Synopsis

Let A be a unital C*-algebra and let B be an abelian C*-subalgebra containing the identity of A. For any pure state h of B let Fh be the set of states of A which restrict to h on B. Necessary and sufficient conditions are given for an element x in A to have the property that, for each h, x is unable to distinguish between distinct elements of Fh. By specializing, this leads to a new proof of a theorem giving necessary and sufficient conditions for Fh to be a singleton for each h.

It is also shown that if A is postliminal and π(B) is a maximal abelian C*-subalgebra of π(B) for each irreducible representation π of A then Fh is a Choquet simplex for each h.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 113 - 122
Copyright
Copyright © Royal Society of Edinburgh 1982

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