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Composition operators on weighted analytic spaces

Part of: Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  17 April 2023

Marouane Bourass ,
Ibrahim Marrhich Open the ORCID record for Ibrahim Marrhich [Opens in a new window]  and
Fouzia Mkadmi
Marouane Bourass
Affiliation:
Faculty of Sciences, Mohammed V University in Rabat, CeReMAR, LAMA, B.P. 1014, Rabat, Morocco e-mail: marouane.bourass@gmail.com fouzia.mkadmii@gmail.com
Ibrahim Marrhich
Affiliation:
Laboratoire Mathématiques Fondamentales et Appliquées, Faculty of Sciences Ain-Chock, Hassan II University of Casablanca, B.P. 5366 Maarif, Casablanca, Morocco e-mail: ibrahim.marrhich@univh2c.ma brahim.marrhich@gmail.com
Fouzia Mkadmi
Affiliation:
Faculty of Sciences, Mohammed V University in Rabat, CeReMAR, LAMA, B.P. 1014, Rabat, Morocco e-mail: marouane.bourass@gmail.com fouzia.mkadmii@gmail.com
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Abstract

We characterize the membership in the Schatten ideals $\mathcal {S}_p$, $0<p<\infty $, of composition operators acting on weighted Dirichlet spaces. Our results concern a large class of weights. In particular, we examine the case of perturbed superharmonic weights. Characterization of composition operators acting on weighted Bergman spaces to be in $\mathcal {S}_p$ is also given.

Keywords

Composition operatorsToeplitz operatorsweighted Bergman spacesweighted Dirichlet spacesSchatten p-ideals

MSC classification

Primary: 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) 30H20: Bergman spaces, Fock spaces 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Secondary: 47B33: Composition operators 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 4 , December 2023 , pp. 1213 - 1230
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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