Abstract
In this paper, positive moment operators on the space C(S) are considered, where S is a compact abelian semigroup possessing a separating set of continuous semicharacters. These operators have the convenient property that every semicharacter is an eigenvector. A criterion on the corresponding set of eigenvalues, the moments, is introduced, which is satised for the moment family of a positive moment operator T if, and only if, T is a Reynolds operator. It is shown that these operators are uniquely determined by a set of semicharacters and corresponding moments, if the semicharacters separate S and the moments are nonzero. In this context, all derivations are characterized, which generate a semigroup and commute with translations. Finally, all positive Reynolds and moment operators on the multiplicative unit interval are determined. Subjclass: Primary 47B38, 47B48, 47B65, 44A60; Secondary 20M14.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
