Hopfs ergodic theorem for nonlinear operators.
Horocyclic products of trees
Let be homogeneous trees with degrees , respectively. For each tree, let be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of is the graph consisting of all -tuples with , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If and then we obtain a Cayley graph of the...
Hyperbolic geometry on noncommutative balls.
Hypercontractivity of simple random variables
The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.
Hypercyclic and chaotic weighted shifts
Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.
Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type
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.