Thickness in topological transformation semigroups.

Haynes, Tyler

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

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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.