Vol. 32, No. 3, 1970

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ISSN: 0030-8730
Geometry of the unit sphere of a Cāˆ—-algebra and its dual

Charles A. Akemann and Bernard Russo

Vol. 32 (1970), No. 3, 575ā€“585
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
Authors
Charles A. Akemann
Bernard Russo