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Hann-Banach-Arveson extension theorem an...
Mohari, Anilesh...

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Hann-Banach-Arveson extension theorem and Kadison isomorphism by Mohari, Anilesh ( Author )
Lemonjar Open Access
Australian National University
26-07-2023
Let $C^*(\cls)$ be the $C^*$ algebra generated by an operator system $\cls$ i.e. a unital $*$-closed subspace of a unital $C^*$ algebra $\cla$. We prove that any complete order isomorphism $\cli:\cls \raro \cls'$ between two such operator systems of matrix algebras has a unique extension to a $C^*$-isomorphism $\cli:C^*(\cls) \raro C^*(\cls')$. However, the same statement with more general operator systems of infinite dimensional $C^*$-algebra is false. As an application of this result, we characterise upto cocycle conjugacy the extreme points of unital completely positive maps on matrix algebra.
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English
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MYR 0.01
1
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http://arxiv.org/abs/1304.6849
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