Invariant subspaces of Voiculescu's circular operator

Details Invariant subspaces of Voiculescu's circular operator Invariant subspaces of Voiculescu's circular operator

2000-04-17

arxiv.org/abs/math/0004104v1

Mathematics

Operator Algebras

45 pages

Scientific paper

We show that Voiculescu's circular operator and, more generally, each
circular free Poisson operator has a continuous family of invariant subspaces
relative to the von Neumann algebra it generates. The proof relies on upper
triangular random matrix models and consequent realizations of these operators
as upper triangular matrices of free random variables.

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