Displaying similar documents to “Extremal Maps of a Hilbert Space Equipped with a Natural Cone.”

On extremal positive maps acting between type I factors

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...

Canonical functional extensions on von Neumann algebras

Carlo Cecchini (1999)

Studia Mathematica

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The topology and the structure of the set of the canonical extensions of positive, weakly continuous functionals from a von Neumann subalgebra M 0 to a von Neumann algebra M are described.