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Normal and Cohyponormal Weighted Composition Operators on H 2

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Operator Theory in Harmonic and Non-commutative Analysis

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 240))

Abstract

In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H 2. We show that if W f,ϕ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ϕ has the Denjoy–Wolff point in the open unit disk, W f,ϕ is cohyponormal if and only if it is normal; in this case, f and ϕ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator W f,ϕ . Finally, we examine the commutant of a cohyponormal weighted composition operator.

Mathematics Subject Classification (2010). 47B20, 47B38, 47B33.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, IUPUI, Indianapolis, Indiana, 46202, USA

    Carl C. Cowen

  2. Institute of Mathematical Sciences, Ewha Womans University, 120-750, Seoul, Korea

    Sungeun Jung

  3. Department of Mathematics, Ewha Womans University, 120-750, Seoul, Korea

    Eungil Ko

Authors
  1. Carl C. Cowen
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  2. Sungeun Jung
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  3. Eungil Ko
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Corresponding author

Correspondence to Carl C. Cowen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, Virginia, USA

    Joseph A. Ball

  2. Department of Mathematics, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kingdom

    Michael A. Dritschel

  3. Department of Mathematics, University of Auckland, Auckland, New Zealand

    A.F.M. ter Elst

  4. Mathematical Sciences Institute, Université Lille 1Villeneuve d'Ascq, France and The Australian National University, Canberra, Aust Capital Terr, Australia

    Pierre Portal

  5. School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

    Denis Potapov

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Cowen, C.C., Jung, S., Ko, E. (2014). Normal and Cohyponormal Weighted Composition Operators on H 2 . In: Ball, J., Dritschel, M., ter Elst, A., Portal, P., Potapov, D. (eds) Operator Theory in Harmonic and Non-commutative Analysis. Operator Theory: Advances and Applications, vol 240. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-06266-2_4

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