Geometry of the unit sphere of a C^∗-algebra and its dual

Charles A. Akemann and Bernard Russo

Vol. 32 (1970), No. 3, 575–585

DOI: 10.2140/pjm.1970.32.575

Abstract

In this study we exploit as a main tool a polar decomposition for linear functionals on operator algebras, introduced in 1958 by Sakai, to determine various types of extremal behavior in the unit spheres of C^∗-algebras and their duals. We discuss exposed points and complex extreme points as well as extreme points.

Mathematical Subject Classification

Primary: 46.65

Milestones

Received: 11 August 1969

Published: 1 March 1970