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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A left ideal of any -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 -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