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Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions

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Abstract.

Multiplication operators in weighted Banach (and locally convex) spaces of functions holomorphic in the unit disc are well known. In this note we investigate the connection between power boundedness, mean ergodicity and uniform mean ergodicity of such operators.

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Authors and Affiliations

  1. Instituto Universitaro de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071, Valencia, Spain

    José Bonet

  2. Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072, Eichstätt, Germany

    Werner J. Ricker

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  1. José Bonet
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  2. Werner J. Ricker
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Correspondence to José Bonet.

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Dedicated to Heinz König on the occassion of his 80th birthday

José Bonet: Support of the Alexander von Humboldt Foundation and MEC and FEDER Project MTM 2007-62643 and GV project Prometeo/2008/101 are gratefully acknowledged.

Received: 13 October 2008, Revised: 18 November 2008

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Bonet, J., Ricker, W.J. Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions . Arch. Math. 92, 428–437 (2009). https://doi.org/10.1007/s00013-009-3061-1

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  • DOI: https://doi.org/10.1007/s00013-009-3061-1

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