Poisson transform for higher-rank graph algebras and its applications

Skalski, A. and Zacharias, J. (2010) Poisson transform for higher-rank graph algebras and its applications. Journal of Operator Theory, 63(2), pp. 425-454.

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Abstract

Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying relations encoded by the graph structure which we call Λ-contractions or Λ-coisometries. Besides commutant lifting results and characterisations of pure states on higher rank graph algebras several applications to the structure theory of non-selfadjoint graph operator algebras are presented generalising recent results in special cases.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Skalski, A., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Operator Theory
Journal Abbr.:J. Operator Th.
ISSN:0379-4024
ISSN (Online):1841-7744

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