65th SAMS Congress
06-08 December 2022
Stellenbosch University
SUN Logo

A Lumer–Phillips type generation theorem for bi-continuous semigroups
Christian Budde, University of the Free State
Sven-Ake Wegner, University of Hamburg

SAMS Subject Classification Number: 3, 10, 11

The famous 1960s Lumer–Phillips theorem states that a closed and densely defined operator A:D(A)XX on a Banach space X generates a strongly continuous contraction semigroup if and only if (A,D(A)) is dissipative and the range of λA is surjective in X for some λ>0. We will investigate 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. This is joint work with S.-A. Wegner (Hamburg, Germany).