Equivalent definitions of positive definiteness

P. H. Maserick and Franciszek Hugon Szafraniec

Vol. 110 (1984), No. 2, 315–324

DOI: 10.2140/pjm.1984.110.315

Abstract

Equivalent conditions for linear functionals, on a commutative algebra 𝒜 with involution, to be positive are proved by elementary methods devoid of disintegration theorems. The theory is applied to present straightforward verifications of, heretofore subtle, equivalences of quadratic form and finite difference definitions of positive definiteness of functions on semigroups.

Mathematical Subject Classification 2000

Primary: 46K99

Secondary: 43A35

Milestones

Received: 22 December 1981

Revised: 30 August 1982

Published: 1 February 1984