Completeness of Inner Product Spaces Associated with Functional on Jordan Structures

Abstract

© 2020, Pleiades Publishing, Ltd. Abstract: We show that a normal functional varphi on a JBW* triple induces, via Gelfand–Naimark–Segal like construction, a complete inner product space if and only if varphi is a finite convex combination of extreme points from the predual. Application of this result to von Neumann algebras is shown.