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 |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Zacharias, Professor 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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