Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Semigroups with positive definite structure
HTML articles powered by AMS MathViewer

by Parfeny P. Saworotnow PDF
Proc. Amer. Math. Soc. 40 (1973), 421-425 Request permission

Abstract:

Let $G$ be a semigroup with the identity 1 and an involution $x \to {x^ \ast }$. One can define a complex-valued and an ${H^ \ast }$-algebra valued positive definite function on $G$ in the obvious way. Assume that for each $x \in G$ there exists a positive number ${L_x}$ such that $q({x^ \ast }x) \leqq {L_x}q(1)$ for each complex positive definite function on $G$. It is shown that each ${H^ \ast }$-algebra valued positive definite function on $G$ is of the form $p(x) = (f,{T_x}f)$ for some representation $T$ of $G$ on a Hilbert module $H$ and $f \in H$. Also there is an analogue of Bochner theorem for $G$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A35, 22A25
  • Retrieve articles in all journals with MSC: 43A35, 22A25
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 40 (1973), 421-425
  • MSC: Primary 43A35; Secondary 22A25
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0320640-1
  • MathSciNet review: 0320640