Certain Invariant Subspaces for Operators with Rich Eigenvaujes

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...

Characteristic Functions and Joint Invariant Subspaces

Let T := [T1, . . . , Tn] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a “one-toone” correspondence between the joint invariant subspaces under T1, . . . , Tn, and the regular factorizations of the characteristic function ΘT associated with T . In particular, we prove that there is a non-trivial joint in...

Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

Abstract: In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspace...

ON p-HYPONORMAL OPERATORS

In this paper we show that p-hyponormal operators with 0 / ∈ σ(|T | 1 2 r ) are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.

On the Existence of Now-trivial Invariant Subspaces for Certain Classes of Operators