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

• [1] B. Basit and A. J. Pryde, Differences of vector-valued functions on topological groups, Proc. Amer. Math. Soc. 124 (1996), 1969-1975.
• [2] B. Basit and A. J. Pryde, Unitary eigenvalues of semigroup homomorphisms, Monash University Analysis Paper 105, May 1997, 8 pp.
• [3] J. P. R. Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), 455-461.
• [4] C. Datry et G. Muraz, Analyse harmonique dans les modules de Banach I: propriétés générales, Bull. Sci. Math. 119 (1995), 299-337.
• [5] N. Dunford, On one parameter groups of linear transformations, Ann. of Math. 39 (1938), 569-573.
• [6] J. A. Goldstein, Extremal properties of contraction semigroups on Hilbert and Banach spaces, Bull. London Math. Soc. 25 (1993), 369-376.
• [7] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc., 1957.
• [8] I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515-531.
• [9] W. Rudin, Fourier Analysis on Groups, Interscience, 1967.
• [10] K. Yosida, Functional Analysis, Springer, 1966.