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 representations. II: The bundle approach

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.