International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 477-489
Doubly stochastic right multipliers
Department of Mathematics, Simon Fraser University, B.C., Burnaby V5A 1S6, Canada
Received 13 June 1983
Copyright © 1984 Choo-Whan Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be the set of normalized regular Borel measures on a compact group . Let be the set of doubly stochastic (d.s.) measures on such that , where , and and are Borel subsets of . We show that there exists a bijection between and such that , where is normalized Haar measure on , and for . Further, we show that there exists a bijection between and , the set of d.s. right multipliers of . It follows from these results that the mapping defined by is a topological isomorphism of the compact convex semigroups and . It is shown that is the closed convex hull of left translation operators in the strong operator topology of .