Integral operators in the theory of induced Banach representation II. The bundle approach

International Journal of Mathematics and Mathematical Sciences

I. E. Schochetman¹ 

[1] Mathematics Department, Oakland University, Rochester 48603, Michigan, USA;

关键词: locally compact group;    Banach representation;    induced representation;    integrated form;    integral operator;    vector field;    cross-section;    continuity structure;    Banach bundle;    quotient topology;    kernel bundle.;   

DOI  :  10.1155/S016117128100046X

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown