AN OPERATOR SPACE CHARACTERIZATION OF DUAL OPERATOR ALGEBRAS

Abstract. 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 algebras) 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. Let A be an operator algebra, that is, a closed subalgebra of B(H) for some Hilbert space H. When A contains the identity operator IH, we say that A is unital and when A is w-closed, we say that it is a dual algebra. In the frame-work of operator space theory, Blecher, Ruan and Sinclair gave a remarkable characterization of unital operator algebras, up to unital complete isometry [6]. Later, Blecher completed the picture by proving an analogous characterization of operator algebras up to complete isomorphism [4]. The purpose of this paper is to solve the open problem of characterizing in a similar way unital dual algebras (resp. dual algebras) up to w-continuous unital complete isometry (resp. com-plete isomorphism). Roughly speaking, we will show that a dual operator algebr