Strong continuity of semigroup homomorphisms

• Autorzy: Bolis Basit , A. J. Pryde
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

representation; semigroup homomorphism; weak continuity; strong continuity; Lipschitz map

Kategorie tematyczne

• 22A25: Representations of general topological groups and semigroups
• 47D03: Groups and semigroups of linear operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 1
• Strony: 71-78

Daty

wydano

1999

otrzymano

1997-09-16

poprawiono

1998-04-28

Twórcy

autor

Bolis Basit

• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia,

autor

A. J. Pryde

• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia,

Bibliografia

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