On a Generalization of the Cauchy Equation (Short Communication)
On a Generalization of the Cauchy Equation.
Un calcul fonctionnel pour les opérateurs linéaires de l'espace hilbertien et certaines de ses applications
Subnormal operators, cyclic vectors and reductivity
Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.
A resolvent condition implying power boundedness
The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.
Contribution en Hongrie à la théorie spectrale des transformations linéaires
On some properties of the function class and applications to Hilbert space operators
Bedingungen für die Multiplikationstabelle eines in sich abgeschlossenen orthogonalen Funktionensystems
Sur un problème pour les polyèdres convexes dans l’espace -dimensionnel
Vibrations d'une corde non homogène
Perturbations des transformations autoadjointes dans l'espace de Hilbert.
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