Minimal Cuntz-Krieger Dilations and Representations of Cuntz-Krieger Algebras

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dc.creatorBhat, B. V. Rajarama
dc.creatorDey, Santanu
dc.creatorZacharias, Joachim
dc.date2005-05-24
dc.date.accessioned2026-07-07T05:20:13Z
dc.date.available2026-07-07T05:20:13Z
dc.descriptionGiven a contractive tuple of Hilbert space operators satisfying certain $A$-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 maximal $A$-relation piece. We define a maximal piece more generally for a finite set of polynomials in $n$ noncommuting variables. We classify all representations of Cuntz-Krieger algebras ${\mathcal O}_A$ obtained from dilations of commuting tuples satisfying $A$-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.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0505499
dc.identifierhttp://arxiv.org/abs/math/0505499
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75298
dc.subjectOperator Algebras
dc.subject47A20;47A13
dc.titleMinimal Cuntz-Krieger Dilations and Representations of Cuntz-Krieger Algebras
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