A characterization of nonunital operator algebras

Author:
Zhong-Jin Ruan

Journal:
Proc. Amer. Math. Soc. **121** (1994), 193-198

MSC:
Primary 47D25; Secondary 46L05, 47D15

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186994-5

MathSciNet review:
1186994

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Abstract | References | Similar Articles | Additional Information

Abstract: We give an abstract matrix norm characterization for operator algebras with contractive approximate identities by using the second dual approach. We show that if *A* is an -Banach pseudoalgebra with a contractive approximate identity, then the second dual of *A* is a unital -Banach pseudoalgebra containing *A* as a subalgebra. It follows from the Blecher-Ruan-Sinclair characterization theorem for unital operator algebras that is completely isometrically unital isomorphic to a concrete unital operator algebra on a Hilbert space. Thus *A* is completely isometrically isomorphic to a concrete nondegenerate operator algebra with a contractive approximate identity.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186994-5

Keywords:
Operator algebras,
-Banach pseudoalgberas,
-matricially normed spaces,
operator duals,
completely bounded maps

Article copyright:
© Copyright 1994
American Mathematical Society