# Strong continuity of semigroup homomorphisms

Studia Mathematica (1999)

- Volume: 132, Issue: 1, page 71-78
- ISSN: 0039-3223

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topBasit, Bolis, and Pryde, A.. "Strong continuity of semigroup homomorphisms." Studia Mathematica 132.1 (1999): 71-78. <http://eudml.org/doc/216586>.

@article{Basit1999,

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).},

author = {Basit, Bolis, Pryde, A.},

journal = {Studia Mathematica},

keywords = {representation; semigroup homomorphism; weak continuity; strong continuity; Lipschitz map; abelian topological semigroups; Lipschitz functions},

language = {eng},

number = {1},

pages = {71-78},

title = {Strong continuity of semigroup homomorphisms},

url = {http://eudml.org/doc/216586},

volume = {132},

year = {1999},

}

TY - JOUR

AU - Basit, Bolis

AU - Pryde, A.

TI - Strong continuity of semigroup homomorphisms

JO - Studia Mathematica

PY - 1999

VL - 132

IS - 1

SP - 71

EP - 78

AB - 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).

LA - eng

KW - representation; semigroup homomorphism; weak continuity; strong continuity; Lipschitz map; abelian topological semigroups; Lipschitz functions

UR - http://eudml.org/doc/216586

ER -

## References

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