ArticleOriginal scientific text
Title
Strong continuity of semigroup homomorphisms
Authors 1, 1
Affiliations
- Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Abstract
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).
Keywords
representation, semigroup homomorphism, weak continuity, strong continuity, Lipschitz map
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Pages:
71-78
Main language of publication
English
Received
1997-09-16
Accepted
1998-04-28
Published
1999
Exact and natural sciences