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arXiv · 1611.03929

Operational extreme points and Cuntz's canonical endomorphism

Marie Choda
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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.

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Marie Choda. 2016-11-12. Operational extreme points and Cuntz's canonical endomorphism. https://arxiv.org/abs/1611.03929

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