\(L_1\)-space for a positive operator affiliated with von Neumann algebra (Q2358778)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_1\)-space for a positive operator affiliated with von Neumann algebra |
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\(L_1\)-space for a positive operator affiliated with von Neumann algebra (English)
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16 June 2017
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Let \(a\) be an injective positive selfadjoint operator affiliated with a von Neumann algebra \(\mathcal M\). The author suggests a construction of an \(L_1\) space, denoted by \(L_1(a)\), associated to \(a\). It is shown that this space is isometrically isomorphic to the predual of \(\mathcal M\). Order properties of this space are studied. A similar construction for a \(C^*\)-algebra \(\mathcal A\) is also considered.
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operator algebra
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von Neumann algebra
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\(C^*\)-algebra
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noncommutative integration
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\(L_1\)-space
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positive operator
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semifinite normal weight
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unbounded operator
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