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Operator Algebras with Contractive Approximate Identities

Published online by Cambridge University Press:  20 November 2018

Yiu-Tung Poon  and
Zhong-Jin Ruan
Yiu-Tung Poon
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
Zhong-Jin Ruan
Affiliation:
Department of Mathematics University of Illinois, Urbana-Champaign Urbana, Illinois 61801 U.S.A.
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Abstract

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We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

Keywords

47D2546H2547D15operator spacesoperator algebrasL∞-matricially normed spacesL∞-Banach algebrasdouble centralizer algebrasM-idealsunitalization algebras
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 397 - 414
Copyright
Copyright © Canadian Mathematical Society 1994

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