When K + (n-4) L fails to be Nef.
M.L. Fania (1993)
Manuscripta mathematica
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M.L. Fania (1993)
Manuscripta mathematica
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Marcin Marciniak (2010)
Banach Center Publications
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The paper is devoted to the problem of classification of extremal positive linear maps acting between 𝔅(𝒦) and 𝔅(ℋ) where 𝒦 and ℋ are Hilbert spaces. It is shown that every positive map with the property that rank ϕ(P) ≤ 1 for any one-dimensional projection P is a rank 1 preserver. This allows us to characterize all decomposable extremal maps as those which satisfy the above condition. Further, we prove that every extremal positive map which is 2-positive turns out to be automatically...
Władysław A. Majewski, Marcin Marciniak (2006)
Banach Center Publications
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A map φ: Mₘ(ℂ) → Mₙ(ℂ) is decomposable if it is of the form φ = φ₁ + φ₂ where φ₁ is a CP map while φ₂ is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map φ: M₂(ℂ) → M₂(ℂ) we construct concrete maps (not necessarily unital) φ₁ and φ₂ which give a decomposition of φ. We also show that in most cases this decomposition is unique.
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Annales Polonici Mathematici
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Annales Polonici Mathematici
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Annales Polonici Mathematici
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