Generators of C0-Semigroups of weighted composition operators

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Gallardo Gutiérrez, Eva A. and Siskakis, Aristomenis G. and Yakubovich, Dmitry (2021) Generators of C0-Semigroups of weighted composition operators. (Unpublished)

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Abstract

We prove that in a large class of Banach spaces of analytic functions inthe unit disc D an (unbounded) operator Af = G · f′ + g · f with G, g analytic in D generates a C0-semigroup of weighted composition operators if and only if it generates a C0-semigroup. Particular instances of such spaces are the classical Hardy spaces. Our result generalizes previous results in this context and it is related to cocycles of flows of analytic functions on Banach spaces. Likewise, for a large class of non-separable Banach spaces X of analytic functions in D contained in the Bloch space, we prove that no non-trivial holomorphic flow induces a C0-semigroup of weighted composition operators on X. This generalizes previous results in [6] and [1] regarding C0-semigroup of (unweighted) composition operators.


Item Type:Article
Uncontrolled Keywords:Weighted composition operators; C0-semigroups; Cocycles of Holomorphic Flows
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:73283
Deposited On:30 Jun 2022 10:48
Last Modified:01 Jul 2022 07:51

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