DT-operators and decomposability of Voiculescu's circular operator

Details DT-operators and decomposability of Voiculescu's circular operator DT-operators and decomposability of Voiculescu's circular operator

2002-05-08

arxiv.org/abs/math/0205077v1

Mathematics

Operator Algebras

58 pages

Scientific paper

The DT-operators are introduced, one for every pair (\mu,c) consisting of a compactly supported Borel probability measure \mu 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 II_1-factor, whose isomorphism class depends only on the number and sizes of atoms of \mu. 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.

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