Continuous Family of Invariant Subspaces for R{diagonal Operators

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

The Singularly Continuous Spectrum and Non-closed Invariant Subspaces

Let A be a bounded self-adjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded self-adjoint perturbations V of A that are off-diagonal with respect to the decomposition H = H0 ⊕H1. In particular, we prove the existence of a oneparameter family of dense no...

The Singular Continuous Spectrum and Non-closed Invariant Subspaces

Let A be a bounded self-adjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded self-adjoint perturbations V of A that are off-diagonal with respect to the decomposition H = H0 ⊕ H1. In particular, we prove the existence of a one-parameter family of dense ...

A Continuous Model for Quainilpotent Operators and Translation Invariant Subspaces in Weighted L^2 of R+

INVARIANT SUBSPACES FOR POLYNOMIALLY COMPACT ALMOST SUPERDIAGONAL OPERATORS ON l(pi)

It is shown that almost superdiagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces if the nonlocally convex linear topology τ(p i) is locally bounded. 1. Introduction. The purpose of this paper is to show that almost super-diagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces ...