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We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms… (More)

The boundedness and compactness of weighted composition operators on the Hardy space H of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schattenclass membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived.… (More)

The norm of a bounded composition operator induced by a disc automorphism is estimated on weighted Hardy spaces H(β) in which the classical Hardy space is continuously embedded. The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence β. As a by-product of our results, an estimate for the norm… (More)

We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators, which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy… (More)

A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on H2 by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not… (More)

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H∞[b : b has finite angular derivative everywhere]. We study the most well-known example of a… (More)

For any simply connected domain Ω, we prove that a Littlewood type inequality is necessary for boundedness of composition operators on Hp(Ω), 1 ≤ p < ∞, whenever the symbols are finitely-valent. Moreover, the corresponding “little-oh” condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for… (More)

- Eva A. Gallardo-Gutiérrez, Pekka J. Nieminen
- J. London Math. Society
- 2015

A remarkable result by Denjoy and Wolff states that every analytic self-map φ of the open unit disc D of the complex plane, except an elliptic automorphism, has an attractive fixed point to which the sequence of iterates {φn}n 1 converges uniformly on compact sets: if there is no fixed point in D, then there is a unique boundary fixed point that does the… (More)

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