A Lumer–Phillips type generation theorem for bi-continuous semigroups
Christian BuddeUniversity of the Free State, Bloemfontein, South Africa
Sven-Ake WegnerUniversität Hamburg, Germany
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. 65–80DOI 10.4171/ZAA/1695