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Embedding of some classes of operators into strongly continuous semigroups

Part of: Special classes of linear operators Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  08 January 2025

Isabelle Chalendar  and
Romain Lebreton
Isabelle Chalendar*
Affiliation:
Université Gustave Eiffel, LAMA (UMR 8050), UPEM, UPEC, CNRS, F-77454 Marne-la-Vallée, France
Romain Lebreton
Affiliation:
Laboratoire Paul Painlevé, Université de Lille, 59655 Villeneuve d’Ascq Cédex France e-mail: romain.lebreton@univ-lille.fr
*
e-mail: isabelle.chalendar@univ-eiffel.fr
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Abstract

In this paper, we study the embedding problem of an operator into a strongly continous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space $H^2$. In particular, we focus on the isometric ones using the necessary and sufficient condition observed by T. Eisner.

Keywords

Semigroupembeddingisometrycomposition operatorToeplitz operator

MSC classification

Primary: 47D03: Groups and semigroups of linear operators 47B33: Composition operators 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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