2007/07/09 by Adam Skalski, Skalski, Adam, Joachim Zacharias +1 · 1 citation
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) #math.FA #math.OA #msc:05C20 #msc:46L05 #msc:47A13 #msc:47A20 #msc:47L75
paper · pdf · doi:10.48550/arxiv.0707.1292
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
openalex publication_date 2007/07/09 · arxiv created 2008/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.