A Lumer–Phillips type generation theorem for bi-continuous semigroups
Christian Budde
University of the Free State, Bloemfontein, South AfricaSven-Ake Wegner
Universität Hamburg, Germany
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Abstract
The famous 1960s Lumer–Phillips theorem states that a closed and densely defined operator on a Banach space generates a strongly continuous contraction semigroup if and only if is dissipative and the range of is surjective in for some . In this paper, we establish a version of this result for bi-continuous semigroups and apply the latter amongst other examples to the transport equation as well as to flows on infinite networks.
Cite this article
Christian Budde, Sven-Ake Wegner, A Lumer–Phillips type generation theorem for bi-continuous semigroups. Z. Anal. Anwend. 41 (2022), no. 1/2, pp. 65–80
DOI 10.4171/ZAA/1695