Characterizing weak-operator continuous linear functionals on \(B(H)\) constructively (Q651258)
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scientific article; zbMATH DE number 5987887
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterizing weak-operator continuous linear functionals on \(B(H)\) constructively |
scientific article; zbMATH DE number 5987887 |
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Characterizing weak-operator continuous linear functionals on \(B(H)\) constructively (English)
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9 December 2011
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Summary: Let \(\mathcal B(H)\) be the space of bounded operators on a not necessarily separable Hilbert space \(H\). Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on \(\mathcal B(H)\) are finite sums of functionals of the form \(T\rightsquigarrow \langle Tx,y\rangle \). We also prove that the identification of weak- and strong-operator continuous linear functionals on \(\mathcal B(H)\) cannot be established constructively.
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constructive
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operators
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ultraweak operator topology
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continuous functionals
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bounded operators
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constructive analysis
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continuous linear functionals
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0.8784132599830627
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0.8569447994232178
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0.7758256793022156
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0.7686108946800232
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