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On generators of C0-semigroups of composition operators

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Gallardo-Gutiérrez, Eva A. and Yakubovich, Dmitry V. (2019) On generators of C0-semigroups of composition operators. Israel Journal of Mathematics, 229 (1). pp. 487-500. ISSN 0021-2172

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Official URL: https://link.springer.com/journal/11856



Abstract

Avicou, Chalendar and Partington proved in [4] that an (unbounded) operator Af = G.f′ on the classical Hardy space generates a C0 semigroup of composition operators if
and only if it generates a quasicontractive semigroup. Here we prove that if such an operator A generates a C0 semigroup, then it is automatically a semigroup of composition operators, so that the condition of quasicontractivity of the semigroup in the cited result is not necessary. Our result applies to a rather general class of Banach spaces of analytic functions in the unit
disc.
1.


Item Type:Article
Uncontrolled Keywords:Teoría de operadores
Palabras clave (otros idiomas):Operator theory, Spaces and algebras of analytic functions, C-semigroups
Subjects:Sciences > Mathematics
ID Code:54659
Deposited On:12 Mar 2019 13:31
Last Modified:12 Mar 2019 13:31

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