Representations of C*-algebras of row-countable graphs and unitary\n equivalence

2019/10/29 by Ben Hur Eidt, Eidt, Ben hur, Danilo Royer +1
Mathematics · #2010: 47L30 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1910.13304

openalex publication_date 2019/10/29 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In this article we show that there are branching systems (which induce\nrepresentations of the graph algebra C^*(E)) associated to each row-countable\ngraph E. For row-countable graphs, we characterize the condition (L) via\nbranching systems. Moreover, we show that each permutative representation in\nHilbert spaces operators is unitarily equivalent to one induced by a branching\nsystem, even the spaces being not separable. Furthermore, under some hypothesis\non the graph, we show that each representation of the graph C*-algebra is\npermutative.\n

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