A bicommutant theorem for dual Banach algebras (Q2837096)
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scientific article; zbMATH DE number 6186283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bicommutant theorem for dual Banach algebras |
scientific article; zbMATH DE number 6186283 |
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10 July 2013
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bicommutant
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dual Banach algebra
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A bicommutant theorem for dual Banach algebras (English)
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Let \(A\) be a unital dual Banach algebra. This means that \(A\) is a dual Banach space such that the multiplication is separately weak\(^*\)-continuous. The author shows that there exist a reflexive Banach space \(E\) and an isometric, weak\(^*\)-weak\(^*\)-continuous homomorphism \(\pi\) from \(A\) into the Banach algebra \(B(E)\) of all bounded linear operators on \(E\) such that \(\pi(A)\) equals the bicommutant of \(\pi(A)\) in \(B(E)\).
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