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The ideal envelope of an operator algebra
Author(s):
David
P.
Blecher;
Masayoshi
Kaneda
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2103-2113.
MSC (2000):
Primary 46L05, 46L07, 47L30;
Secondary 46H10, 47L75
Posted:
January 27, 2004
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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:
10.1090/S0002-9939-04-07303-4
PII:
S 0002-9939(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
Posted:
January 27, 2004
Additional Notes:
This research was supported by a grant from the National Science Foundation
Communicated by:
David R. Larson
Copyright of article:
Copyright
2004,
American Mathematical Society
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