Operadores sobre espacios de sucesiones infraperiódicas con valores vectoriales (II).
Opérateurs diagonaux dans les espaces à bases.
Operators commuting with the shift on sequence spaces.
Operators on spaces of analytic functions
Let be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that is polynomially bounded if for every polynomial p. We give necessary and sufficient conditions for to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.
Operators with absolute continuity properties: an application to quasinormality
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.
Operators with hypercyclic Cesaro means
An operator T on a Banach space ℬ is said to be hypercyclic if there exists a vector x such that the orbit is dense in ℬ. Hypercyclicity is a strong kind of cyclicity which requires that the linear span of the orbit is dense in ℬ. If the arithmetic means of the orbit of x are dense in ℬ then the operator T is said to be Cesàro-hypercyclic. Apparently Cesàro-hypercyclicity is a strong version of hypercyclicity. We prove that an operator is Cesàro-hypercyclic if and only if there exists a vector...
Operators with shift generating by a compact Lie group.
Order properties of the space of finitely additive transition functions.
Order properties of the space of strongly additive transition functions.
Orthogonal constant mappings in isosceles orthogonal spaces
p-Analytic and p-quasi-analytic vectors
For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.
Perturbation results on semi-Fredholm operators and applications.
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
Polynomial approximations and universality
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Positivity in the theory of supercyclic operators
A bounded linear operator T defined on a Banach space X is said to be supercyclic if there exists a vector x ∈ X such that the projective orbit {λTⁿx : λ ∈ ℂ, n ∈ ℕ} is dense in X. The aim of this survey is to show the relationship between positivity and supercyclicity. This relationship comes from the so called Positive Supercyclicity Theorem. Throughout this exposition, interesting new directions and open problems will appear.
Properties of the slant weighted Toeplitz operator.
Pseudo shift operators with large images
We give suitable conditions for the existence of many holomorphic functions f on a disc such that the image of any nonempty open subset under the action of pseudo shift operators on f is arbitrarily large. This generalizes an earlier result about images of derivatives and completes another one on infinite order differential operators.
Reducible representations of abelian groups
A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted spaces on locally compact abelian groups, for even weights and .
Relations Between Summing Norms of Mappings on ln... .
Sätze vom Mazur-Orlicz-Typ