Integral Equations and Operator Theory

, Volume 84, Issue 4, pp 487–500 | Cite as

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.

Keywords

Isometries Averaging operators 

Mathematics Subject Classification

Primary 46E30 Secondary 46B04 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Applied Mathematics IV, EPSEVGPolytechnical University of CataloniaVilanova i GeltrúSpain
  2. 2.Department of Applied Mathematics and AnalysisUniversity of BarcelonaBarcelonaSpain

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