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*-representations on Banach *-algebras

Author: A. K. Gaur
Journal: Proc. Amer. Math. Soc. 126 (1998), 1461-1466
MSC (1991): Primary 46K15, 46H15
MathSciNet review: 1389519
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Abstract: We study notions of $g$-bounded linear functionals and represent-
able functionals on Banach *-algebras. An equivalence between these two is established for general Banach *-algebras. In particular, we characterize $g$-bounded linear functionals on Banach *-algebras with approximate identity and isometric involution. In addition, we prove a result on representation of $g$-bounded positive linear functionals in terms of cyclic vectors for the corresponding *-representation.

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A. K. Gaur
Affiliation: Department of Mathematics, Duquesne University, Pittsburgh, Pennsylvania 15282

Keywords: Banach *-algebra, $g$-bounded linear functionals, representable functional, *-representation
Received by editor(s): October 16, 1995
Received by editor(s) in revised form: February 14, 1996, August 19, 1996, September 10, 1996, and October 25, 1996
Additional Notes: This research is supported by the Presidential Scholarship Award, 1995–96
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society