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Numerical ranges in locally M-convex algebras. I

Part of: Topological (rings and) algebras with an involution Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Thanassis Chryssakis
Thanassis Chryssakis
Affiliation:
Mathematical Institute, University of Athens, 57, Solonos Street, Athens 10679, Greece
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Abstract

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The bidual of a unital infrabarrelled l.m.c. C* algebra E, equipped with the bidual topology and the regualr Arens product, is always an l.m.c. C*-algebra. On the other hand, a unital l.m.c. *-algebra E has the C*-property if and only if every self-adjoint element x of E is strongly hermitian (x has real numerical range), or the sets of normalized states and normalized continuous positive linear forms of E coincide. Finally, every unital cpmplete l.m.c. C* algebra satisfying, locally, the property ‘the extreme points are dense in that set of continuous positive linear forms” (antiliminal algebra) has the complexes as its only normal elements.

Keywords

numerical rangenormalized statesI.m.c. *-algebraI.m.c. C*-akgebra.

MSC classification

Secondary: 46H99: None of the above, but in this section 46K99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 304 - 316
Copyright
Copyright © Australian Mathematical Society 1986

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