Model theory of a non-degenerate representation of a unital C*-algebra

2010/10/29 by Argoty, Camilo
#03C45 #03C65 #03C98 #46L08 #46L30 #46L51 #46L52 #46L89 #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Operator Algebras (math.OA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1010.6188

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 give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. We show that for every v in H the type of v over the empmtyset is in correspondence with the positive linear functional over A defined by v and has quantifier elimination as well. Finally, we characterize the model companion of the incomplete theory of all non-degenerate representations of A.

Related

• Model theory of C^*-algebras
• Quantifier elimination in C*-algebras
• An Introduction To Continuous Model Theory
• On New Approach to Fredholm theory in unital C*-algebras
• Model Theory of Operator Systems and C^*-Algebras