Strong continuity of semigroup homomorphisms
Basit, Bolis ; Pryde, A.
Studia Mathematica, Tome 133 (1999), p. 71-78 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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).

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216586 
@article{bwmeta1.element.bwnjournal-article-smv132i1p71bwm,
     author = {Bolis Basit and A. Pryde},
     title = {Strong continuity of semigroup homomorphisms},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {71-78},
     zbl = {0924.22002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p71bwm}
}

Basit, Bolis; Pryde, A. Strong continuity of semigroup homomorphisms. Studia Mathematica, Tome 133 (1999) pp. 71-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p71bwm/

[00000] [1] B. Basit and A. J. Pryde, Differences of vector-valued functions on topological groups, Proc. Amer. Math. Soc. 124 (1996), 1969-1975. | Zbl 0852.43001

[00001] [2] B. Basit and A. J. Pryde, Unitary eigenvalues of semigroup homomorphisms, Monash University Analysis Paper 105, May 1997, 8 pp.

[00002] [3] J. P. R. Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), 455-461. | Zbl 0472.54007

[00003] [4] C. Datry et G. Muraz, Analyse harmonique dans les modules de Banach I: propriétés générales, Bull. Sci. Math. 119 (1995), 299-337. | Zbl 0840.43005

[00004] [5] N. Dunford, On one parameter groups of linear transformations, Ann. of Math. 39 (1938), 569-573. | Zbl 0019.26604

[00005] [6] J. A. Goldstein, Extremal properties of contraction semigroups on Hilbert and Banach spaces, Bull. London Math. Soc. 25 (1993), 369-376. | Zbl 0794.47025

[00006] [7] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc., 1957. | Zbl 0078.10004

[00007] [8] I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515-531. | Zbl 0294.54010

[00008] [9] W. Rudin, Fourier Analysis on Groups, Interscience, 1967.

[00009] [10] K. Yosida, Functional Analysis, Springer, 1966.