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*-representations on Banach *-algebras

Author(s): A. K. Gaur
Journal: Proc. Amer. Math. Soc. 126 (1998), 1461-1466.
MSC (1991): Primary 46K15, 46H15
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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.

References:

1.
J. Dixmier, Les $C^*$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. MR 30:1404

2.
E. G. Effros, A decomposition theory for representations of $C^*$-algebras, Trans. Amer. Math. Soc. 107 (1963), 83-106. MR 26:4202

3.
J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. MR 29:1547

4.
A. K. Gaur, A characterization of representable functionals on complex Banach *-algebras, submitted, 1995.

5.
C. E. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, NJ, 1960. MR 22:5903

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Additional Information:

A. K. Gaur
Affiliation: Department of Mathematics, Duquesne University, Pittsburgh, Pennsylvania 15282
Email: gaur@mathcs.duq.edu

DOI: 10.1090/S0002-9939-98-03846-5
PII: S 0002-9939(98)03846-5
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
Copyright of article: Copyright 1998, American Mathematical Society

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