Displaying similar documents to “A mean ergodic theorem for a contraction semigroup in Lebesgue space”

Strong continuity of semigroup homomorphisms

Bolis Basit, A. Pryde (1999)

Studia Mathematica

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Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).