On generators of $C_0$-semigroups of composition operators
Functional Analysis
2019-08-01 v1
Abstract
Avicou, Chalendar and Partington proved that an (unbounded) operator on the classical Hardy space generates a semigroup of composition operators if and only if it generates a quasicontractive semigroup. Here we prove that if such an operator generates a 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.
Keywords
Cite
@article{arxiv.1708.02259,
title = {On generators of $C_0$-semigroups of composition operators},
author = {Eva A. Gallardo-Gutiérrez and Dmitry Yakubovich},
journal= {arXiv preprint arXiv:1708.02259},
year = {2019}
}