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Operator system

Wikipedia contributorsAdapted for Fathomly · View authors
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Source updated May 6, 2024

Given a unital C*-algebra {\mathcal {A}}, a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace {\mathcal {M}}\subseteq {\mathcal {A}} of a unital C*-algebra an operator system via S:={\mathcal {M}}+{\mathcal {M}}^{*}+\mathbb {C} 1.

The appropriate morphisms between operator systems are completely positive maps.

By a theorem of Choi and Effros, operator systems can be characterized as *-vector spaces equipped with an Archimedean matrix order.

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This article is adapted from the Wikipedia article “Operator system”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Operator space

In functional analysis, a discipline within mathematics, an operator space is a normed vector space "given together with an isometric embedding into the space B(H) of all bounded operators on a Hilbert space H.". The appropriate morphisms between operator spaces are completely bounded maps.