On positive linear maps preserving invertibility (Q801266)
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scientific article; zbMATH DE number 3877812
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On positive linear maps preserving invertibility |
scientific article; zbMATH DE number 3877812 |
Statements
On positive linear maps preserving invertibility (English)
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1984
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A positive linear map \(\Phi\) between two \(C^*\)-algebras is a Jordan homomorphism if \(\Phi\) preserves invertibility and the range of \(\Phi\) is a \(C^*\)-algebra. A counterexample is given for the case that the range of \(\Phi\) is not assumed to be a \(C^*\)-algebra; this answers a question raised by \textit{B. Russo} [Proc. Am. Math. Soc. 17, 1019-1022 (1966; Zbl 0166.400)].
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positive linear map
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Jordan homomorphism
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