Submission date: 28 October 2010.

Abstract:

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We show this theory, in an appropiate language, has quantifier elimination and it is superstable. We show that for every v in H, the type of v over the empty set is in correspondence with the positive linear functional over A defined by v. Finally, we characterize forking, orthogonality and domination of types and show the theory has weak elimination of imaginaries.

Mathematics Subject Classification: 03C45, 03C65, 03C98, 46L08, 46L30, 46L51, 46L52, 46L89.

Keywords and phrases: C*-algebras, representation theory, stability.

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