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Positive Isometric Averaging Operators on \({\ell^2(\mathbb{Z}, \mu)}\)

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Abstract

We show that positive isometric averaging operators on the sequence space \({\ell^2(\mathbb{Z}, \mu)}\) are determined by very subtle arithmetic conditions on \({\mu}\) (even for very simple examples), contrary to what happens in the continuous case \({L^2({\mathbb{R}}^+)}\), where any possible average value is realized by a suitable positive isometry.

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Authors and Affiliations

  1. Department of Applied Mathematics IV, EPSEVG, Polytechnical University of Catalonia, 08880, Vilanova i Geltrú, Spain

    Santiago Boza

  2. Department of Applied Mathematics and Analysis, University of Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Javier Soria

Authors
  1. Santiago Boza
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  2. Javier Soria
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Correspondence to Santiago Boza.

Additional information

S. Boza and J. Soria have been partially supported by the Spanish Government Grant MTM2013-40985-P and the Catalan Autonomous Government Grant 2014SGR289.

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Boza, S., Soria, J. Positive Isometric Averaging Operators on \({\ell^2(\mathbb{Z}, \mu)}\) . Integr. Equ. Oper. Theory 84, 487–500 (2016). https://doi.org/10.1007/s00020-016-2284-3

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  • DOI: https://doi.org/10.1007/s00020-016-2284-3

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