Poisson transform for higher-rank graph algebras and its applications

Adam Skalski; Joachim Zacharias

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arXiv · 0707.1292

Poisson transform for higher-rank graph algebras and its applications

Adam Skalski·Joachim Zacharias

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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.

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Adam Skalski, Joachim Zacharias. 2008-06-16. Poisson transform for higher-rank graph algebras and its applications. https://arxiv.org/abs/0707.1292

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