Poisson transform for higher-rank graph algebras and its applications
Operator Algebras
2008-06-16 v3 Functional Analysis
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 -contractions or -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.
Cite
@article{arxiv.0707.1292,
title = {Poisson transform for higher-rank graph algebras and its applications},
author = {Adam Skalski and Joachim Zacharias},
journal= {arXiv preprint arXiv:0707.1292},
year = {2008}
}
Comments
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