We consider the topological space of composition operators C(H2) on the Hardy space H2(D) of the unit disc D with operator norm topology. We prove a necessary condition for two composition operators to lie in the same path components and as a consequence we are able to determine path components of composition operators induced by analytic self-maps of the unit disc D which are analytic in a nei...

Abstract This paper characterises the boundedness and compactness of Agler–McCarthy monomial operators by reducing them to weighted composition deriving explicit Carleson measure criteria on half-plane. The results are illustrated examples.

We provide examples of the product of two localization operators. As a special case, we study the composition of Gabor multipliers. The results highlight the instability of this product and underline the necessity of expressing it in terms of asymptotic expansions. We study the problem of calculating or estimating the product of two localization operators. The motivation comes either from signa...

Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas σ1, σ2, and σ3, the composition problem is to find an equivalent mapping over only σ1 and σ3. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many σ2 symbols as possible, even if not all can be eliminated. It c...

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

We investigate the shape of the numerical range for composition operators on the Hardy space H of the unit disc. As is usually the case when one studies composition operators, interesting questions arise from the interplay between the theories of analytic functions and linear operators.

We obtain new and simple characterizations for the boundedness and compactness of weighted composition operators on the Fock space over C. We also describe all weighted composition operators that are normal or isometric.

We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given.