Strong continuity of semigroup homomorphisms

Volume 132 / 1999

Bolis Basit, A. Pryde Studia Mathematica 132 (1999), 71-78 DOI: 10.4064/sm-132-1-71-78


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).


  • Bolis Basit
  • A. Pryde

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