International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 625-640
doi:10.1155/S016117128100046X
Integral operators in the theory of induced Banach representation II. The bundle approach
Mathematics Department, Oakland University, Rochester 48603, Michigan, USA
Received 4 March 1981
Copyright © 1981 I. E. Schochetman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let G be a locally compact group, H a closed subgroup and L a Banach representation of H. Suppose U is a Banach representation of G which is induced by L. Here, we continue our program of showing that certain operators of the integrated form of U can be written as integral operators with continuous kernels. Specifically, we show that: (1) the representation space of a Banach bundle; (2) the above operators become integral operators on this space with kernels which are continuous cross-sections of an associated kernel bundle.