Geodesic
Strong continuity of semigroup homomorphisms
Studia Mathematica, Tome 132 (1999) no. 1, pp. 71-78

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/sm-132-1-71-78
Keywords: representation, semigroup homomorphism, weak continuity, strong continuity, Lipschitz map

Bolis Basit 1 ; A. Pryde 1

1 
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Bolis Basit; A. Pryde. Strong continuity of semigroup homomorphisms. Studia Mathematica, Tome 132 (1999) no. 1, pp. 71-78. doi: 10.4064/sm-132-1-71-78

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