Invariant subspaces of the quasinilpotent DT-operator Academic Article uri icon

abstract

  • In [4] we introduced the class of DT-operators, which are modeled by certain upper triangular random matrices, and showed that if the spectrum of a DT-operator is not reduced to a single point, then it has a nontrivial, closed, hyperinvariant subspace. In this paper, we prove that also every DT-operator whose spectrum is concentrated on a single point has a nontrivial, closed, hyperinvariant subspace. In fact, each such operator has a one-parameter family of them. It follows that every DT-operator generates the von Neumann algebra L(F2) of the free group on two generators. © 2003 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Dykema, K., & Haagerup, U.

citation count

  • 15

complete list of authors

  • Dykema, Ken||Haagerup, Uffe

publication date

  • April 2004