Linear Analysis Seminar

Date: March 3, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Ken Dykema, Texas A&M University

Title: Commuting operators in finite von Neumann algebras

Abstract: We find a joint spectral distribution measure for families of commuting elements of a finite von Neumann algebra. This generalizes the Brown measure for single operators. Furthermore, we find a lattice (based on Borel sets) consisting of hyperinvariant projections that decompose the spectral distribution measure. This leads to simultaneous upper triangularization results for commuting operators and behaves well with multivariate holomorphic functional calculus. (Joint work with Ian Charlesworth, Fedor Sukochev and Dmitriy Zanin.)