Geometric Aspects of $C^{\ast }$-Extreme Points

Abstract

We provide a characterization of the $C^{\ast }$-extreme points of the closed unit ball of a von Neumann algebra and demonstrate that $C^{\ast }$-extremality is equivalent to both linear extremality and strong extremality. As an application, we characterize certain classes of von Neumann algebras in terms of their $C^{\ast }$-extreme points.

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