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Recurrent Linear Operators

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A Publisher's Erratum to this article was published on 25 January 2015

Abstract

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.

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Authors and Affiliations

  1. Department of Mathematics, University of Crete, Knossos Avenue, 714 09 , Heraklion, Crete, Greece

    George Costakis

  2. Fakultät für Mathematik, SFB 701, Universität Bielefeld, Postfach 100131, 33501 , Bielefeld, Germany

    Antonios Manoussos

  3. Department of Mathematics, Aalto University, P. O. Box 11100, 00076 , Aalto, Finland

    Ioannis Parissis

Authors
  1. George Costakis
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  2. Antonios Manoussos
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  3. Ioannis Parissis
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Corresponding author

Correspondence to Ioannis Parissis.

Additional information

Communicated by Vladimir Müller.

A.M. is fully supported by SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathematik” at the University of Bielefeld, Germany.

I.P. is supported by the Academy of Finland, grant 138738.

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Costakis, G., Manoussos, A. & Parissis, I. Recurrent Linear Operators. Complex Anal. Oper. Theory 8, 1601–1643 (2014). https://doi.org/10.1007/s11785-013-0348-9

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