Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.

In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every “normalized” subnormal operator S such that either {(S∗nSn)1/n} does not converge in the SOT to the identity operator or {(SnS∗n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subsp...

The question whether every operator on H has an hyperinvariant subspace is one of the most difficult problems in operator theory. The purpose of this paper is to make a beginning on the hyperinvariant subspace problems for another class of operators closely related to the normal operators namely, the class of k -quasi-class A operators. A necessary and sufficient condition for the hypercyclicit...

If f is an endomorphism of a finite dimensional vector space over a field K then an invariant subspace X ⊆ V is called hyperinvariant (respectively, characteristic) if X is invariant under all endomorphisms (respectively, automorphisms) that commute with f . According to Shoda (Math. Zeit. 31, 611–624, 1930) only if |K| = 2 then there exist endomorphisms f with invariant subspaces that are char...

We prove the existence of a non-trivial hyperinvariant subspace for several sets polynomially compact operators. The main results paper are: (i) norm closed algebra $$\mathcal {A}\subseteq \mathcal {B}(\mathscr {X})$$ which consists quasinilpotent operators has subspace; (ii) if there exists non-zero operator in closure generated by an band {S}$$ , then subspace.

It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single-valued extension property.

This paper deals with local spectral properties of Extended Hamilton operators and their adjoint operators. The relationship between the (strongly decomposability, hyperinvariant subspace problem, etc.) corresponding is obtained.

It is shown that to every operator T in a general von Neumann factor M of type II1 and to every Borel set B in the complex plane C, one can associate a maximal, closed, T -invariant subspace, K = KT (B), affiliated with M, such that the Brown measure of T |K is concentrated on B. Moreover, K is T -hyperinvariant, and the Brown measure of PK⊥T |K⊥ is concentrated on C \ B. In particular, if T ∈ ...