Lipschitz operators

Abstract

Let ( B, G, U) denote a continuous isometric representation of the Lie group G on the Banach space B . Further let B n denote the C n-elements of the representation and ∥ · ∥ n the corresponding C n -norm. We prove that if K; B ∞↦ B is dissipative and satisfies the Lipschitz condition ‖( U( g) KU( g) −1− K) a‖⩽ c| g|·‖ a‖ 1, a∈ B ∞, | g|<1, then its closure K generates a C 0 -semigroup of contractions T. Moreover, T leaves invariant the Lipschitz spaces which interpolate between B and B 1.