Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-12T20:33:44.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Module Homomorphisms of the Dual Modules of Convolution Banach Algebras

Published online by Cambridge University Press:  20 November 2018

F. Ghahramani  and
J. P. Mcclure
F. Ghahramani
Affiliation:
Department of Mathematics and Astronomy University of Manitoba Winnipeg, Manitoba R3T 2N2
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Suppose that A is either the group algebra L1 (G) of a locally compact group G, or the Volterra algebra or a weighted convolution algebra with a regulated weight. We characterize: a) Module homomorphisms of A*, when A* is regarded an A** left Banach module with the Arens product, b) all the weak*-weak* continuous left multipliers of A**.

Keywords

43A2246H25.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 180 - 185
Copyright
Copyright © Canadian Mathematical Society 1992 

Footnotes

The research of the authors was supported by NSERC grants OGP003664 and A8069, respectively.

References

1. Bade, W. G. and Dales, H. G., Norms and ideals in radical convolution algebras, J. Funct. Anal. 41(1981), 77–109.Google Scholar
2. Curtis, P. C. and Figa-Talamanca, A., Factorization theorems for Banach algebras. In: Function algebras, Proc. Int. Symps. on Function Algebras, Talman, 1965, Scott Foresman, Chicago, 1966.Google Scholar
3. Duncan, J. and Hosseiniun, S. A. R., The second dual of a Banach algebra, Proc. Royal Soc. Edinburgh, 84A(1979), 309–325.Google Scholar
4. Dunford, N. and Schwartz, J. T., Linear operators I, Wiley (1958), New York.Google Scholar
5. Ghahramani, F., Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc. (2) 21(1980), 149–161.Google Scholar
6. Ghahramani, F. and Lau, A. T., Isometric isomorphisms between the second conjugate algebras of group algebras, Bull. London Math. Soc. 20(1988), 342–344.Google Scholar
7. Ghahramani, F., Lau, A. T. and Losert, V., Isometric isomorphisms between Banach algebras related to locally compact groups, Trans. Amer. Math. Soc. (1) 321(1990), 273–283.Google Scholar
8. Hewitt, E. and Ross, K. A., Abstract harmonic Analysis, 1, Springer, Berlin, 1963.Google Scholar
9. Isik, N. and Pym, J. and A. Ùlger, The second dual of the group algebra of a compact group, J. London Math. Soc. 35(1987), 135–148.Google Scholar
10. Kamowitz, H. and Scheinberg, S., Derivations and automorphisms of L1(0,1), Trans. Amer. Math. Soc. 135(1969), 415–427.Google Scholar
11. Lau, A. T., Operators which commute with convolutions on subspaces of L∞(G), Colloq. Math. 39(1978), 351–359.Google Scholar
12. Lau, A. T., Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups, Math. Proc. Camb. Phil. Soc. 99(1986), 273–283.Google Scholar
13. Lau, A. T. and Losert, V., On the second conjugate algebra of L1 (G) of a locally compact group, J. London Math. Soc. (2) 37(1988), 464–470.Google Scholar
14. Lau, A. T. and Pym, J., Concerning the second dual of the group algebra of a locally compact group, J. London Math. Soc. (2) 41(1990), 445–460.Google Scholar
15. Wendel, J. G., Left centralizers and isomorphisms of groups algebras, Pacific J. Math. 2(1952), 251–261.Google Scholar
16. Wong, J. C. S., Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc. 144(1969), 351–363.Google Scholar