Arveson's extension theorem in *-algebras

G. H. Esslamzadeh; L. Turowska

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arXiv · 1311.5065

Arveson's extension theorem in *-algebras

G. H. Esslamzadeh·L. Turowska

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Abstract

Arveson's extension theorem asserts that B(H) is an injective object in the category of operator systems. Calling every self adjoint unital subspace of a unital *-algebra, a quasi operator system, we show that Arveson's theorem remains valid in the much larger category of quasi operator systems. This shows that Arveson's theorem as a non commutative extension of Hahn-Banach theorem, is of purely algebraic nature.

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G. H. Esslamzadeh, L. Turowska. 2013-11-20. Arveson's extension theorem in *-algebras. https://arxiv.org/abs/1311.5065

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