Minimal Cuntz-Krieger dilations and representations of Cuntz-Krieger algebras

Bhat, B.V.R., Dey, S. and Zacharias, J. (2006) Minimal Cuntz-Krieger dilations and representations of Cuntz-Krieger algebras. Proceedings Mathematical Sciences, 116(2), pp. 193-220. (doi: 10.1007/BF02829787)

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Given a contractive tuple of Hilbert space operators satisfying certainA-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger dilation can be obtained from the classical minimal isometric dilation as a certain maximalA-relation piece. We define a maximal piece more generally for a finite set of polynomials inn noncommuting variables. We classify all representations of Cuntz-Krieger algebrasO <sub>A</sub> obtained from dilations of commuting tuples satisfyingA-relations. The universal properties of the minimal Cuntz-Krieger dilation and the WOT-closed algebra generated by it is studied in terms of invariant subspaces.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Zacharias, Professor Joachim
Authors: Bhat, B.V.R., Dey, S., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings Mathematical Sciences
ISSN (Online):0973-7685

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