On C*-Extreme Maps and *-Homomorphisms of a Commutative C*-Algebra

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dc.creatorGregg, M. C.
dc.date2009-02-09
dc.date2009-02-12
dc.date.accessioned2026-07-07T12:40:28Z
dc.date.available2026-07-07T12:40:28Z
dc.descriptionThe generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. In this paper we show that a C*-extreme point of S_H(C(X)) satisfies a certain spectral condition on the operators in the range of the associated positive operator-valued measure. This result enables us to show that C*-extreme maps from C(X) into K^+, the algebra generated by the compact and scalar operators, are multiplicative. This generalizes a result of D. Farenick and P. Morenz. We then determine the structure of these maps.
dc.descriptionminor change to proof of Theorem 5, 12 pages, To appear in Integral Equations and Operator Theory
dc.identifierhttps://arxiv.org/abs/0902.1453
dc.identifierhttp://arxiv.org/abs/0902.1453
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219453
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L05; 46L30
dc.titleOn C*-Extreme Maps and *-Homomorphisms of a Commutative C*-Algebra
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