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Mean Ergodic Multiplication Operators on Weighted Spaces of Continuous Functions

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Abstract

Multiplication operators on weighted Banach spaces and locally convex spaces of continuous functions have been thoroughly studied. In this note, we characterize when continuous multiplication operators on a weighted Banach space and on a weighted inductive limit of Banach spaces of continuous functions are power bounded, mean ergodic or uniformly mean ergodic. The behaviour of the operator on weighted inductive limits depends on the properties of the defining sequence of weights and it differs from the Banach space case.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, 46022, Valencia, Spain

    José Bonet, Enrique Jordá & Alberto Rodríguez

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  1. José Bonet
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  2. Enrique Jordá
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  3. Alberto Rodríguez
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Correspondence to José Bonet.

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Bonet, J., Jordá, E. & Rodríguez, A. Mean Ergodic Multiplication Operators on Weighted Spaces of Continuous Functions. Mediterr. J. Math. 15, 108 (2018). https://doi.org/10.1007/s00009-018-1150-8

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  • DOI: https://doi.org/10.1007/s00009-018-1150-8

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