Arveson’s Extension Theorem for Conditionally Unital Completely Positive Maps
Pub Date : 2024-07-11
DOI:10.1134/s0081543824010218
引用次数: 0
Abstract
Conditionally unital completely positive maps are used to characterize generators of unital completely positive semigroups on \(C^*\)-algebras. In this work, a generalization of this notion is proposed that includes maps between different operator systems. In terms of this generalization, conditionally unital completely positive maps are infinitesimal increments of unital completely positive maps. The basic properties of conditionally unital completely positive maps are studied, the Choi–Jamiołkowski duality is established, and an Arveson-type extension theorem for completely bounded conditionally unital completely positive maps is proved in the case of maps with values in finite-dimensional \(C^*\)-algebras.
有条件单元完全正映射的阿维森扩展定理
摘要 条件单整全正映射被用来描述 \(C^*\)-gebras 上的单整全正半群的生成器。在这项工作中，我们提出了这一概念的广义化，其中包括不同算子系统之间的映射。根据这一概括，有条件单整全正映射是单整全正映射的无穷小增量。研究了有条件空完全正映射的基本性质，建立了崔-贾米奥乌科夫斯基对偶性，并在映射值在有限维 \(C^*\)-代数中的情况下证明了完全有界有条件空完全正映射的阿维森型扩展定理。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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