An order characterization of commutativity for \(C^{\ast}\)-algebras (Q2701613)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An order characterization of commutativity for \(C^{\ast}\)-algebras |
scientific article |
Statements
19 February 2001
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commutativity for \(C^{\ast}\)-algebras
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operator-monotonic increasing function
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positive element
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Ogasawara's order characterization theorem
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exponential function
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operator-monotone increasing
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An order characterization of commutativity for \(C^{\ast}\)-algebras (English)
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The author uses Ogasawara's order characterization theorem to show that a \(C^*\)-algebra \(A\) is commutative if and only if the exponential function defined on the set of nonnegative real numbers is operator-monotone increasing on \(A\).
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