Poisson transform for higher-rank graph algebras and its applications

Details Poisson transform for higher-rank graph algebras and its applications Poisson transform for higher-rank graph algebras and its applications

2007-07-09

arxiv.org/abs/0707.1292v3

Mathematics

Operator Algebras

25 pages; v3 corrects a definition of a doubly commuting $\Lambda$-contraction and adds a reference. The paper will appear in

Scientific paper

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.

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