Representations of C*-algebras in dual and right dual Banach algebras

Spain, P. G. (2015) Representations of C*-algebras in dual and right dual Banach algebras. Houston Journal of Mathematics, 41(1), pp. 231-263.

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Abstract

The range of a contractive algebra morphism from a C*-algebra to a Banach algebra is closed, and the morphism is a C*-morphism onto its range. When the codomain is a dual Banach algebra, or only a right dual Banach algebra, such a morphism extends to a W*-morphism onto the weak star closure of the range (at least in the unital case). Boolean algebras of contractive projections (in right dual Banach algebras) have weak star completions; and operators with a contractive functional calculus on a dual Banach space are scalar type prespectral. Some of these results extend to morphisms that are neither unital nor contractive, so long as one can renorm the codomain dually in a suitable manner, as when the codomain is a dual Banach algebra, or when the range of the natural extension of the morphism forms a commuting set.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Spain, Dr Philip
Authors: Spain, P. G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Houston Journal of Mathematics
Publisher:University of Houston
ISSN:0362-1588

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