Hypercyclic operators in Fréchet spaces.
Hypercyclic operators with an infinite dimensional closed subspace of periodic points.
Let X be an infinite dimensional separable Banach space. There exists a hypercyclic operator on X which is equal to the identity operator on an infinite dimensional closed subspace of X.
Hypercyclic sequences of operators
A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study when a sequence...
Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces
Our aim in this paper is to prove that every separable infinite-dimensional complex Banach space admits a topologically mixing holomorphic uniformly continuous semigroup and to characterize the mixing property for semigroups of operators. A concrete characterization of being topologically mixing for the translation semigroup on weighted spaces of functions is also given. Moreover, we prove that there exists a commutative algebra of operators containing both a chaotic operator and an operator which...
Hypercyclicity of convolution operators on spaces of entire functions
In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables
Hypercyclicity of Semigroups is a Very Unstable Property
Hypercyclicity of C0-semigroups is a very unstable property: We give examples to show that adding arbitrary small constants or a bounded rank one operator to the generator of a hypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (even in operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limit of nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, the restriction of a hypercyclic...
Hypercyclicity of special operators on Hilbert function spaces
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
Hyperinvariant subspace lattice of isometries
Hyperinvariant subspace lattice of some -contractions
Hyperinvariant subspace lattice of weak contractions
Hyperinvariant subspaces and extended eigenvalues.
Hyperinvariant subspaces for some operators on locally convex spaces.
Hyperinvariant subspaces of operators on Hilbert spaces
Hyperinvariante Teilräume kompakter Operatoren in topologischen Vektorräume.
Hyperinvariante Teilräume stetiger Abbildungen in topologischen Vektorräumen.
Hyperinvariante Teilräume vollstetiger Abbildungen in topologischen Vektorräumen
Hyperreflexive operators on finite dimensional Hilbert spaces
In this paper a complete characterization of hyperreflexive operators on finite dimensional Hilbert spaces is given.
Hyperreflexivity of bilattices
The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice we can construct the bilattice . Similarly, having a bilattice we may consider the lattice . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive...
Hypersingular Marcinkiewicz integrals along surface with variable kernels on Sobolev space and Hardy-Sobolev space.
Hypoellipticité et paramétrix pour des opérateurs pseudodifférentiels à caractéristiques doubles