Poisson transform for higher-rank graph algebras and its applications

2007/07/09 by Adam Skalski, Skalski, Adam, Joachim Zacharias +1
Mathematics · #05C20 #46L05 #47A13 #47A20 (Primary) #47L75 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0707.1292

openalex publication_date 2007/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Regular dilations of representations of product systems
• Subalgebras of C*-algebras

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