Poisson transform for higher-rank graph algebras and its applications
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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.
25 pages; v3 corrects a definition of a doubly commuting $Λ$-contraction and adds a reference. The paper will appear in the Journal of Operator Theory
25 pages; v3 corrects a definition of a doubly commuting $Λ$-contraction and adds a reference. The paper will appear in the Journal of Operator Theory