Invariant subspaces of Voiculescu's circular operator

Invariant Subspaces of Voiculescu's Circular Operator

0 Invariant Subspaces of Voiculescu ’ S Circular Operator

The invariant subspace problem relative to a von Neumann algebra M ⊆ B(H) asks whether every operator T ∈ M has a proper, nontrivial invariant subspace H0 ⊆ H such that the orthogonal projection p onto H0 is an element of M; equivalently, it asks whether there is a projection p ∈ M, p / ∈ {0, 1}, such that Tp = pTp. Even when M is a II1–factor, this invariant subspace problem remains open. In t...

Invariant Subspaces and Spectral Conditions on Operator Semigroups

0. Introduction. Let H be a complex Hilbert space of finite or infinite dimension, and let E be a collection of bounded linear operators on H. We say E is reducible if there exists a subspace of H, closed by definition and different from the trivial subspaces {0} and H which is invariant under every member of E . We call E triangularizable if the set of invariant subspaces under E contains a ma...

Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

Perturbation of invariant subspaces ∗

We consider two different theoretical approaches for the problem of the perturbation of invariant subspaces. The first approach belongs to the standard theory. In that approach the bounds for the norm of the perturbation of the projector are proportional to the norm of perturbation matrix, and inversely proportional to the distance between the corresponding eigenvalues and the rest of the spect...