Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra

Details Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra

2006-05-10

arxiv.org/abs/math/0605251v1

Mathematics

Operator Algebras

50 pages

Scientific paper

In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R-diagonal operators in this class. As a particular case, we determine the Brown measure of z=xy^{-1}, where (x,y) is a circular system in the sense of Voiculescu, and we prove that for all positive integers n, z^n is in L^p(M) iff 0

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