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On Operators Generated by Maps with Separable Dynamics

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Geometric Methods in Physics

Part of the book series: Trends in Mathematics ((TM))

Abstract

Weighted shift operator generated by mapping \(\alpha :{X}\rightarrow {X}\) is an operator of the form \(Bu(x)=a_0(x)u(\alpha(x))\),where a 0 is a given function. Spectral properties of such operators are considered.

Mapping α is said to be compatible (with one-sided invertibility) if there exists a function a 0 such that operator B –λI is one-sided invertible for a certain spectral value λ. The main results are a dynamical description of the compatible mappings and one-sided invertibility conditions of B –λI.

Mathematics Subject Classification (2010). Primary 47B38, 47A10.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Białystok, Akademicka 2, PL-15-267, Białystok, Poland

    A. Antonevich

  2. Belarus State University, Nezavisimosti 4, 220030, Minsk, Belarus

    A. Akhmatova

Authors
  1. A. Antonevich
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  2. A. Akhmatova
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Corresponding author

Correspondence to A. Antonevich .

Editor information

Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Mexico City, Distrito Federal, Mexico

    Piotr Kielanowski

  2. Dept. of Mathematics and Statistics, Concordia University, Montreal, Québec, Canada

    S. Twareque Ali

  3. Department of Mathematics - MC J415, Brock University, St. Catharines, Ontario, Canada

    Alexander Odesskii

  4. Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  5. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  6. School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

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Antonevich, A., Akhmatova, A. (2013). On Operators Generated by Maps with Separable Dynamics. In: Kielanowski, P., Ali, S., Odesskii, A., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0645-9_15

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