On the continuity of the map \(\phi\) \(\to | \phi |\) from the predual of a \(W^*\)-algebra (Q1070495)
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scientific article; zbMATH DE number 3935767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the continuity of the map \(\phi\) \(\to | \phi |\) from the predual of a \(W^*\)-algebra |
scientific article; zbMATH DE number 3935767 |
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On the continuity of the map \(\phi\) \(\to | \phi |\) from the predual of a \(W^*\)-algebra (English)
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1984
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Let \(\phi\),\(\psi\) be elements of the predual of a \(W^*\)-algebra. Then \[ \| | \phi | -| \psi | \| \leq (2\| \phi +\psi \| \| \phi -\psi \|)^{1/2}. \] This estimate is best possible. The proof uses the theory of noncommutative \(L^ p\)-spaces.
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predual of a \(W^*\)-algebra
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noncommutative \(L^ p\)-spaces
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