CQ*-algebras and noncommutative measure

Abstract

In this paper we continue the investigations in [4], [5], [8], [13], [14], [15], and [19], of the structure of quasi *-algebras and extend the results in [1] and [2]. Here, noncommutative Tp-spaces are shown to constitute examples of a class of Banach C*-modules called CQ*-algebras. Moreover, it is shown that any (strongly) *-semisimple proper CQ*-algebra (X ,A), with A a separable C*-algebra, can be represented as a CQ*-algebra of type Tp.