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 with respect to a directed system of seminorms and a range condition.