MPS-RR 2000-12
March 2000

Invariant Subspaces of Voiculescu's Circular Operator

Uffe Haagerup

Ken Dykema

Abstract

From the introduction:

In this paper we show that the circular operator and each circular free Poisson operator (defined below) has a continuous family of invariant subspaces relative to the von Neumann algebra it generates. These operators arise naturally in free probability theory, (see the book [17]), and each generates the von Neumann algebra II_1-factor L(F_2) associated to the nonabelian free group on two generators.

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