On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space
Volume 130 / 1998
Studia Mathematica 130 (1998), 1-7
DOI: 10.4064/sm-130-1-1-7
Abstract
Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.
