A characterization of operator algebras

David P. Blecher, Zhong Jin Ruan, Allan M. Sinclair

Research output: Contribution to journalArticlepeer-review


An operator algebra is a uniformly closed algebra of bounded operators on a Hilbert space. In this paper we give a characterization of unital operator algebras in terms of their matricial norm structure. More precisely if A is an L-matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1, then there is a completely isometric isomorphism of A onto a unital operator algebra. Indeed the multiplication on A need not be assumed to be associative for this conclusion to follow. Examples are given to show that the condition on the identity is necessary. It follows from the above that the quotient of an operator algebra by a closed two-sided ideal (with the natural matricial structure) is again an operator algebra up to complete isometric isomorphism.

Original languageEnglish (US)
Pages (from-to)188-201
Number of pages14
JournalJournal of Functional Analysis
Issue number1
StatePublished - Mar 1 1990

ASJC Scopus subject areas

  • Analysis


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