Simultaneous upper triangular forms for commuting operators in a finite\n von Neumann algebra

2017/03/16 by Ian Charlesworth, Charlesworth, Ian, Ken Dykema +5 · 1 citation
Mathematics · #47A60 #47C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1703.05695

openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The joint Brown measure and joint Haagerup--Schultz projections for tuples of\ncommuting operators in a von Neumann algebra equipped with a faithful tracial\nstate are investigated, and several natural properties are proved for these. It\nis shown that the support of the joint Brown measure is contained in the Taylor\njoint spectrum of the tuple, and also in the ostensibly smaller left Harte\nspectrum. A simultaneous upper triangularization result for finite commuting\ntuples is proved and the joint Brown measure and joint Haagerup--Schultz\nprojections are shown to be have well under the Arens multivariate holomorphic\nfunctional calculus of such a commuting tuple.\n

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