Contractive homomorphisms of measure algebras and Fourier algebras
Volume 209 / 2012
Studia Mathematica 209 (2012), 135-150
MSC: Primary 43A20, 43A10, 43A30, 43A22; Secondary 43A25.
DOI: 10.4064/sm209-2-3
Abstract
We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms $\varphi : L^1(F) \rightarrow M(G)$ between group/measure algebras fails to hold in the dual, Fourier/Fourier–Stieltjes algebra, setting. We characterize the contractive $w^*\hbox {-}w^*$ continuous homomorphisms between measure algebras and (reduced) Fourier–Stieltjes algebras. We consider the problem of describing all contractive homomorphisms $\varphi : L^1(F) \rightarrow L^1(G)$.
