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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of nonunital operator algebras
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by Zhong-Jin Ruan PDF
Proc. Amer. Math. Soc. 121 (1994), 193-198 Request permission

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 ${L^\infty }$-Banach pseudoalgebra with a contractive approximate identity, then the second dual ${A^{ \ast \ast }}$ of A is a unital ${L^\infty }$-Banach pseudoalgebra containing A as a subalgebra. It follows from the Blecher-Ruan-Sinclair characterization theorem for unital operator algebras that ${A^{ \ast \ast }}$ 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
  • © Copyright 1994 American Mathematical Society
  • 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