DT-operators and decomposability of Voiculescu's circular operator

By K. Dykema, Uffe Haagerup. 2002

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The DT-operators are introduced, one for every pair (μ, c ) consisting of a compactly supported Borel probability measure μ on the complex plane and a constant c 0. These are operators on Hilbert space that are defined as limits in *-moments of certain upper triangular random matrices. The DT-operators include Voiculescu's circular operator and elliptic deformations of it, as well as the circular free Poisson operators. We show that every DT-operator is strongly decomposable. We also show that a DT-operator generates a II1 -factor, whose isomorphism class depends only on the number and sizes of atoms of μ. Those DT-operators that are also R-diagonal are identified. For a quasi-nilpotent DT-operator T , we find the distribution of T*T and a recursion formula for general *-moments of T .

Subfields: Algebra and Number Theory, Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ae718e270b40c4cbb89ff4f58e20fc078f6f9833

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In Algebra and Number Theory

In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Brown measures of unbounded operators affiliated with a finite von Neumann algebra (2006, methodology): “It was computed in a number of special cases in [9], [2], [5], and [1].”