On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space

Tom 130 / 1998

Driss Drissi Studia Mathematica 130 (1998), 1-7 DOI: 10.4064/sm-130-1-1-7


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.


  • Driss Drissi

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