Poisson transform for higher-rank graph algebras and its applications

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 $\Lambda$-contractions or $\Lambda$-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 $\Lambda$-contraction and adds a reference. The paper will appear in the Journal of Operator Theory

References in corpus (2)

• Operator algebras associated with unitary commutation relations
• Regular dilations of representations of product systems

Cited by in corpus (1)

• Representations of Higher Rank Graph Algebras