Bishop ’ S Property ( Β ) , Hypercyclicity and Hyperinvariant Subspaces
نویسندگان
چکیده
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 hypercyclicity of the adjoint of a quasi-class A operator is also presented. Mathematics subject classification (2010): 47B20, 47A15.
منابع مشابه
Hyperinvariant subspaces and quasinilpotent operators
For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors. We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors. Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector, and so $T$ has a nontrivial hyperinvariant subspace.
متن کاملHyperinvariant Subspaces for Some Operators on Locally Convex Spaces
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.
متن کاملHyperinvariant Subspaces for Some Subnormal Operators
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...
متن کاملLinear Transformations with Characteristic Subspaces That Are Not Hyperinvariant
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...
متن کاملHyperinvariant Subspaces for Some B–circular Operators
We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra vN(A) that is generated by A, is independent of the representation of vN(A), thought of as an abstract W∗–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces of ce...
متن کامل