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Which Weighted Composition Operators are Complex Symmetric?

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake the study of complex symmetric weighted composition operators, identifying several new classes of such operators.

Mathematics Subject Classification (2010). 47B33, 47B32, 47B99.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Pomona College, Claremont, California, 91711, USA

    Stephan Ramon Garcia

  2. Department of Mathematics, Connecticut College, 270 Mohegan Avenue, New London, CT, 06320, USA

    Christopher Hammond

Authors
  1. Stephan Ramon Garcia
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  2. Christopher Hammond
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Corresponding author

Correspondence to Stephan Ramon Garcia .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    HĂĄkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes RodrĂ­guez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Garcia, S.R., Hammond, C. (2014). Which Weighted Composition Operators are Complex Symmetric?. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_10

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