Analysis Seminar
Ken Dykema, Texas A & M University
"Commuting operators in finite von Neumann algebras"
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.