*-representations on Banach *-algebras
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- by A. K. Gaur PDF
- Proc. Amer. Math. Soc. 126 (1998), 1461-1466 Request permission
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
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Additional Information
- A. K. Gaur
- Affiliation: Department of Mathematics, Duquesne University, Pittsburgh, Pennsylvania 15282
- Email: gaur@mathcs.duq.edu
- 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, 1995â96
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1461-1466
- MSC (1991): Primary 46K15, 46H15
- DOI: https://doi.org/10.1090/S0002-9939-98-03846-5
- MathSciNet review: 1389519