Operational extreme points and Cuntz's canonical endomorphism

2016/11/12 by Marie Choda, Choda, Marie
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1611.03929

openalex publication_date 2016/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the fact that the Cuntz algebra O_n is generated by the operators consisting of a finite operatorional partition, we study the notion of operational extreme points (which we introduce here) by using several completely positive maps on O_n. As a typical example, we show that the Cuntz's canonical endomorphism Phi_n is an operational extreme point in the set of completely positive maps on O_n and that it induces a completely positive map which is extreme but not operational extreme, etc.

Related

• Operational extreme points of unital completely positive maps
• Automorphisms of the Cuntz algebras
• C^*-extreme points of unital completely positive maps on real C^*-algebras
• Endomorphisms of B(H)
• Endomorphisms of B(H), extensions of pure states, and a class of representations of O_n