Extreme positive linear maps on \(C^ *\)-algebras (Q1094641)
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scientific article; zbMATH DE number 4026137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extreme positive linear maps on \(C^ *\)-algebras |
scientific article; zbMATH DE number 4026137 |
Statements
Extreme positive linear maps on \(C^ *\)-algebras (English)
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1988
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Let A be a unital \(C^ *\)-algebra and let B be a von Neumann algebra. Let S(A,B) be the convex set of unital positive linear maps between A and B. We prove that the extreme points of S(A,B) are exactly the unital algebra homomorphisms if and only if A is abelian and, either B is abelian or dim A\(<3\).
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unital \(C^ *\)-algebra
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von Neumann algebra
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convex set of unital positive linear maps
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extreme points
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unitial algebra homomorphisms
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