0000000000040464

AUTHOR

Ted Eklund

showing 2 related works from this author

Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

2017

Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

Discrete mathematicsMathematics::Functional AnalysisApplied MathematicsTopological tensor product010102 general mathematicsEberlein–Šmulian theoremWeakly compact operatorBloch type spaceBanach manifoldFinite-rank operator01 natural sciences010101 applied mathematicsEssential normWeighted spaces of analytic functionsFréchet spaceWeighted composition operatorInterpolation spaceBirnbaum–Orlicz space0101 mathematicsLp spaceAnalysisMathematics
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Königs eigenfunction for composition operators on Bloch and H∞ type spaces

2017

Abstract We discuss when the Konigs eigenfunction associated with a non-automorphic selfmap of the complex unit disc that fixes the origin belongs to Banach spaces of holomorphic functions of Bloch and H ∞ type. In the latter case, our characterization answers a question of P. Bourdon. Some spectral properties of composition operators on H ∞ for unbounded Konigs eigenfunction are obtained.

Pure mathematicsMathematics::Complex VariablesComposition operatorApplied Mathematics010102 general mathematicsMathematical analysisBanach spaceHolomorphic functionComposition (combinatorics)EigenfunctionType (model theory)Characterization (mathematics)01 natural sciences010101 applied mathematicsComputer Science::Discrete Mathematics0101 mathematicsUnit (ring theory)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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