Norm decreasing homomorphisms between group algebras

J. E. Kerlin, Wilfred Pepe
1975 Pacific Journal of Mathematics  
The norm decreasing homomorphisms φ of L λ (F) into M(G) for locally compact groups F and G have been characterized by F. P. Greenleaf using an integral representation. In this note the authors improve and unify some of the results and proofs of structure theorems in the previous literature. Necessary and sufficient conditions that φ have a canonical factorization of a general type are expressed in terms of the extensibility of a ^-associated character on a ^-related closed normal subgroup. In
more » ... articular, an explicit factorization of ψ can be obtained when either F or G is Abelian. Also investigated is the structure of norm decreasing homomorphisms ψ with range in
doi:10.2140/pjm.1975.57.445 fatcat:rhhk42tgwncofl5btoq54gb3cq