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Proceedings of the American Mathematical Society

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The ideal envelope of an operator algebra


Authors: David P. Blecher and Masayoshi Kaneda
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2103-2113
MSC (2000): Primary 46L05, 46L07, 47L30; Secondary 46H10, 47L75
DOI: https://doi.org/10.1090/S0002-9939-04-07303-4
Published electronically: January 27, 2004
MathSciNet review: 2053983
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Abstract | References | Similar Articles | Additional Information

Abstract: A left ideal of any $C^*$-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here that operator algebras with a r.c.a.i. should be studied in terms of a certain left ideal of a $C^*$-algebra. We study operator algebras and their multiplier algebras from the perspective of ``Hamana theory'' and using the multiplier algebras introduced by the first author.


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Additional Information

David P. Blecher
Affiliation: Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77204-3008
Email: dblecher@math.uh.edu

Masayoshi Kaneda
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: mkaneda@math.uci.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07303-4
Keywords: Operator algebra, nonselfadjoint algebra, ideals
Received by editor(s): November 5, 2001
Received by editor(s) in revised form: April 16, 2003
Published electronically: January 27, 2004
Additional Notes: This research was supported by a grant from the National Science Foundation
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society