LAUSR

We introduce and study “norm-multiplicative” homomorphisms φ : L1(F ) → Mr(G) between group and measure algebras, and φ : L(ωF ) → M(ωG) between Beurling group and measure algebras, where F and G are locally compact groups with continuous weights ωF and ωG. Through a unified approach we recover, and sometimes strengthen, many of the main known results concerning homomorphisms and isomorphisms between these (Beurling) group and measure algebras. We provide a first description of all positive homomorphisms φ : L1(F ) → Mr(G). We state versions of our results that describe a variety of (possibly unbounded) homomorphisms φ : CF → CG for (discrete) groups F and G. Primary MSC codes: 43A20, 43A10, 43A15, 43A22, 16S34