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Group Algebra Modules. I

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
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Some time ago, J. G. Wendel proved that the operators on the group algebra L1(G) which commute with convolution correspond in a natural way to the measure algebra M(G) (13). One might ask if Wendel's theorem can be restated in a more general setting. It is this question that is the point of departure for our present paper. Let K be a Banach module over L1(G). Our interest is in operators from L1(G) into K, and from K into L∞(G), which commute with the module composition (where L∞(G) is thought of as a module over L1(G) also). Such operators we call (L1(G), K)- and (K, L∞(G))-homomorphisms, respectively. Investigations of various other kinds of module homomorphisms occur in A. Figà-Talamanca (6) and B. E. Johnson (9; 10).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 133 - 150
Copyright
Copyright © Canadian Mathematical Society 1967

References

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