Characterizations of Hilbert space and the Vidav-Palmer theorem (Q370867)
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scientific article; zbMATH DE number 6209841
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterizations of Hilbert space and the Vidav-Palmer theorem |
scientific article; zbMATH DE number 6209841 |
Statements
Characterizations of Hilbert space and the Vidav-Palmer theorem (English)
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20 September 2013
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A formally stronger result than Ptak's inequality for elements of a Hermitian Banach \(*\)-algebra is proved. With this new numerical range tool, a much simplified proof of the Vidav-Palmer theorem is obtained. This new approach allows the author to give new proofs of Ptak's characterization of \(C^*\)-algebras and Berkson's characterizations of Hilbert spaces. Besides, a very simple proof of a ``version'' of the Kawada-Kakutani-Mackey theorem is given.
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Hermitian element
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\(C^*\)-algebra
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Vidav-Palmer theorem
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Hilbert space
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