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  "body": "\n## Summary\n\nAn operator system is a subspace of a unital C*-algebra that contains the unit and is closed under taking adjoints.\nSuch a subspace has enough positive elements to make sense of positive and [[completely positive maps|CGY299QMC3]] on it.\nOperator systems are the setting of the Arveson extension theorem and of much of the theory of completely positive maps.\nA closed operator system is in particular an [[operator space|VB1J9AA4WX]].\n\n## Explanations\n\n### L1 human\n\nInside an algebra of operators, an operator system keeps just enough structure to talk about positivity.\nIt must contain the identity, and with each element it must contain the adjoint.\nIt need not be closed under multiplication.\nFor example, the functions $a + b z + c \\bar z$ on the unit circle, with $a, b, c$ complex, form an operator system in the continuous functions on the circle.\n",
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