A note on the Lumer--Phillips theorem for bi-continuous semigroups

Abstract

Given a Banach space $X$ and an additional coarser Hausdorff locally convex topology $\tau$ on $X$ we characterise the generators of $\tau$-bi-continuous semigroups in the spirit of the Lumer--Phillips theorem, i.e. by means of dissipativity w.r.t.~a directed system of seminorms and a range condition.

References in corpus (2)

• On equicontinuity and tightness of bi-continuous semigroups
• A Lumer-Phillips type generation theorem for bi-continuous semigroups

Cited by in corpus (2)

• Mixed topologies on Saks spaces of vector-valued functions
• Weighted composition semigroups on spaces of continuous functions and their subspaces