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 τ on X we characterise the generators of τ-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.

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