Vol. 57, No. 2, 1975

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Norm decreasing homomorphisms between group algebras

J. E. Kerlin and Wilfred Dennis Pepe

Vol. 57 (1975), No. 2, 445–451

The norm decreasing homomorphisms φ of L1(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 φ-associated character on a φ-related closed normal subgroup. In particular, an explicit factorization of φ can be obtained when either F or G is Abelian. Also investigated is the structure of norm decreasing homomorphisms φ with range in L1(G).

Mathematical Subject Classification 2000
Primary: 43A20
Secondary: 43A22
Received: 27 December 1973
Published: 1 April 1975
J. E. Kerlin
Wilfred Dennis Pepe