A characterization of \(C^*\)-algebras via positive operators (Q1112297)
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scientific article; zbMATH DE number 4078033
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of \(C^*\)-algebras via positive operators |
scientific article; zbMATH DE number 4078033 |
Statements
A characterization of \(C^*\)-algebras via positive operators (English)
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1989
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If B is a \(C^*\)-algebra an application of the Russo-Dye theorem shows that for all unital Banach algebras A with isometric involution each linear unital positive operator T:A\(\to B\) attains its operator norm at the unit element. We prove that this property in fact characterizes \(C^*\)-algebras in the class of all unital Banach *-algebras.
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\(C^*\)-algebra
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Russo-Dye theorem
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isometric involution
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linear unital positive operator
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operator norm
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