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.
Bellomonte, G., Triolo, S. (2012). CQ*-algebras and noncommutative measure. In M.S. Mongiovì, M. Sciacca (a cura di), Bollettino di matematica pura e applicata - Volume V (pp. 79-90). Palermo : ARACNE.
CQ*-algebras and noncommutative measure
BELLOMONTE, Giorgia;TRIOLO, Salvatore
2012-01-01
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.
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