PROBABILITY-MEASURES ON GROUPS AND SOME RELATED IDEALS IN GROUP-ALGEBRAS

Let G be a locally compact group. Random walks on G, some factorization problems in L1(G) and the significance for these of the amenability of G are studied. These topics are linked in this paper via ideals in L1(G) of the form [L1(G) * (δe - μ)] -, where μ is a probability measure on G. Cohen's factorization theorem and some ideas from ergodic theory play an important part. © 1990.