Non-unital operator systems that are dual spaces

2022/06/09 by Yu-Shu Jia, Jia, Yu-Shu, Chi–Keung Ng +1 · 1 citation
Mathematics · #46L07 #47L07 #47L25 #47L50 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2206.04297

openalex publication_date 2022/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will give an abstract characterization of an arbitrary self-adjoint weak^*-closed subspace of L(H) (equipped with the induced matrix norm, the induced matrix cone and the induced weak^*-topology). In order to do this, we obtain a matrix analogues of a result of Bonsall for ^*-operator spaces equipped with closed matrix cones. On our way, we observe that for a ^*-vector X equipped with a matrix cone (in particular, when X is an operator system or the dual space of an operator system), a linear map ϕ:X→ M_n is completely positive if and only if linear functional [x_i,j]_i,j↦ ∑_i,j=1ⁿ ϕ(x_i,j)_i,j on M_n(X) is positive.

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• Predual and tight operator systems

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