The model theory of modules of a C*-algebra

Archive for Mathematical Logic 52 (5-6):525-541 (2013)

Abstract
We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ 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. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an homeomorphism between the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$
Keywords Hilbert space   C*-algebra representation  Model theory  Stability theory  Types
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DOI 10.1007/s00153-013-0330-2
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References found in this work BETA

Hilbert Spaces Expanded with a Unitary Operator.Camilo Argoty & Alexander Berenstein - 2009 - Mathematical Logic Quarterly 55 (1):37-50.

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Citations of this work BETA

Forking and Stability in the Representations of a C*-Algebra.Camilo Argoty - 2015 - Journal of Symbolic Logic 80 (3):785-796.

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