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DT-operators and decomposability of Voiculescu's circular operator
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 126, Number 1, February 2004
- pp. 121-189
- 10.1353/ajm.2004.0004
- Article
- Additional Information
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.