Doubly Stochastic Right Multipliers

Resource type
Date created
1984
Authors/Contributors
Abstract
Let P(G) be the set of normalized regular Borel measures on a compact group G. Let Dr be the set of doubly stochastic (d.s.) measures λ on G×G such that λ(As×Bs)=λ(A×B), where s∈G, and A and B are Borel subsets of G. We show that there exists a bijection μ↔λ between P(G) and Dr such that ϕ−1=m⊗μ, where m is normalized Haar measure on G, and ϕ(x,y)=(x,xy−1) for x,y∈G. Further, we show that there exists a bijection between Dr and Mr, the set of d.s. right multipliers of L1(G). It follows from these results that the mapping μ→Tμ defined by Tμf=μ∗f is a topological isomorphism of the compact convex semigroups P(G) and Mr. It is shown that Mr is the closed convex hull of left translation operators in the strong operator topology of B[L2(G)].
Document
Published as
International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 477-489
http://dx.doi.org/10.1155/S016117128400051X
Publication title
International Journal of Mathematics and Mathematical Sciences
Document title
Doubly Stochastic Right Multipliers
Date
1984
Volume
7
Issue
3
First page
477
Last page
489
Publisher DOI
10.1155/S016117128400051X
Copyright statement
Copyright is held by the author(s).
Permissions
You are free to copy, distribute and transmit this work under the following conditions: You must give attribution to the work (but not in any way that suggests that the author endorses you or your use of the work); You may not use this work for commercial purposes.
Scholarly level
Peer reviewed?
Yes
Language
Member of collection
Attachment Size
140352.pdf 3.72 MB