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Positivity

, Volume 23, Issue 1, pp 177–193 | Cite as

Multiplier and averaging operators in the Banach spaces \(\mathbf{ces(p), \, 1< p < \infty }\)

  • Angela A. Albanese
  • José BonetEmail author
  • Werner J. Ricker
Article

Abstract

The Banach sequence spaces ces(p) are generated in a specified way via the classical spaces \( \ell _p, 1< p < \infty .\) For each pair \( 1< p,q < \infty \) the (pq)-multiplier operators from ces(p) into ces(q) are known. We determine precisely which of these multipliers is a compact operator. Moreover, for the case of \( p = q \) a complete description is presented of those (pp)-multiplier operators which are mean (resp. uniform mean) ergodic. A study is also made of the linear operator C which maps a numerical sequence to the sequence of its averages. All pairs \( 1< p,q < \infty \) are identified for which C maps ces(p) into ces(q) and, amongst this collection, those which are compact. For \( p = q ,\) the mean ergodic properties of C are also treated.

Keywords

Banach sequence spaces ces(pMultiplier Compact operator Cesàro operator Mean ergodic operator 

Mathematics Subject Classification

Primary 46B45 47B37 Secondary 46B42 46G10 47A16 47B10 

Notes

Acknowledgements

The research of the first two authors was partially supported by the Project MTM2016-76647-P (Spain). The second author thanks the Mathematics Department of the Katholische Universität Eichstätt-Ingolstadt (Germany) for its support and hospitality during his research visit in the period September 2016–July 2017.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica “E. De Giorgi”Università del SalentoLecceItaly
  2. 2.Instituto Universitario de Matemática Pura y Aplicada IUMPAUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.Math.-Geogr. FakultätKatholische Universität Eichstätt-IngolstadtEichstättGermany

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