Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T01:03:39.062Z Has data issue: false hasContentIssue false
  • English
  • Français

Group Algebra Modules. II

Published online by Cambridge University Press:  20 November 2018

S. L. Gulick ,
T. S. Liu  and
A. C. M. Van Rooij
S. L. Gulick
Affiliation:
University of Maryland, University of Massachusetts, and R. C. University, Nijmegen, The Netherlands
T. S. Liu
Affiliation:
University of Maryland, University of Massachusetts, and R. C. University, Nijmegen, The Netherlands
A. C. M. Van Rooij
Affiliation:
University of Maryland, University of Massachusetts, and R. C. University, Nijmegen, The Netherlands
Rights & Permissions [Opens in a new window]

Extract

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.

The present paper began as a natural outgrowth of our first paper, where we characterized the module homomorphisms from group algebras into a fairly restrictive class of group algebra modules. We now investigate module homomorphisms from group algebras into a more general class of group algebra modules. Although the two papers are thus related, they can be read quite independently.

Section 2 contains our extension, Theorem 2.1, of P. J. Cohen's theorem on factorization in Banach algebras (1). Our extension is to Banach modules over Banach algebras equipped with an approximate identity. We should mention first that J.-K. Wang observed the existence of such a generalization, and secondly, that our proof requires no ideas different from those in Cohen's proof. Nevertheless, we include a proof that condenses the original proof considerably.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 151 - 173
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Cohen, P. J., Factorization in group algebras, Duke Math. J., 26 (1959), 199–205.Google Scholar
2. Gulick, S. L., Liu, T. S., and van Rooij, A. C. M., Group algebra modules, I, Can. J. Math. (this issue).Google Scholar
3. Hewitt, E. and Ross, K. A., Abstract harmonic analysis, Part I (Berlin, 1963).Google Scholar
4. Macbeath, A. M. and Świerczkowski, S., Inherited measures, Proc. Roy. Soc. Edinburgh, 65 (1961), 237–246.Google Scholar
5. Pontryagin, L. S., Topologische Gruppen, I (Leipzig, 1957).Google Scholar
6. Rudin, W., Measure algebras on abelian groups, Bull. Amer. Math. Soc., 65 (1959), 227–247 Google Scholar