Vol. 110, No. 2, 1984

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Equivalent definitions of positive definiteness

P. H. Maserick and Franciszek Hugon Szafraniec

Vol. 110 (1984), No. 2, 315–324
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
Authors
P. H. Maserick
Franciszek Hugon Szafraniec