On generators of C 0-semigroups of composition operators

Avicou, Chalendar and Partington proved in 2015 [5] 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,...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 229; no. 1; pp. 487 - 500
Main Authors Gallardo-Gutiérrez, Eva A, Yakubovich, Dmitry V
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2019
Subjects
Analytic functions
Banach spaces
Composition
Mathematical analysis
Mathematics
Operators
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Summary:Avicou, Chalendar and Partington proved in 2015 [5] 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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-018-1815-9