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Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1767–1778 | Cite as

Quasinormal and Hyponormal Weighted Composition Operators on \(H^2\) and \(A^2_{\alpha }\) with Linear Fractional Compositional Symbol

  • Mahsa Fatehi
  • Mahmood Haji Shaabani
  • Derek Thompson
Article
First Online:

Abstract

In this paper, we study quasinormal and hyponormal composition operators \(W_{\psi ,\varphi }\)  with linear fractional compositional symbol \(\varphi \) on the Hardy and weighted Bergman spaces. We characterize the quasinormal composition operators induced on \(H^{2}\) and \(A_{\alpha }^{2}\) by these maps and many such weighted composition operators, showing that they are necessarily normal in all known cases. We eliminate several possibilities for hyponormal weighted composition operators but also give new examples of hyponormal weighted composition operators on \(H^2\) which are not quasinormal.

Keywords

Weighted composition operator Composition operator Hyponormal Quasinormal 

Mathematics Subject Classification

47B33 
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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Mahsa Fatehi
    • 1
  • Mahmood Haji Shaabani
    • 2
  • Derek Thompson
    • 3
  1. 1.Department of Mathematics, Shiraz BranchIslamic Azad UniversityShirazIran
  2. 2.Department of MathematicsShiraz University of TechnologyShirazIran
  3. 3.Department of MathematicsTaylor UniversityUplandUSA

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