An operator space characterization of dual operator algebras. (English) Zbl 0926.47054

Le Merdy, Christian

Am. J. Math. 121, No. 1, 55-63 (1999).

Summary: This paper is devoted to dual algebras, that is \(w^*\)-closed algebras of bounded operators on Hilbert space. We give abstract characterizations of unital dual algebras (resp. dual algebra) up to \(w^*\)-homeomorphic unital complete isometry (resp. complete isomorphism). The results we obtain are natural \(w^*\)-versions of analogous characterizations due to Blecher-Ruan-Sinclair and Blecher respectively, in the category of operator algebras.

MSC:

47L45	Dual algebras; weakly closed singly generated operator algebras
46L05	General theory of \(C^*\)-algebras

Keywords:

operator space; dual algebras; \(w^*\)-homeomorphic unital complete isometry; category of operator algebras