Spectral synthesis for \(A(G)\) and subspaces of \(VN(G)\) (Q2731917)
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scientific article; zbMATH DE number 1626792
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral synthesis for \(A(G)\) and subspaces of \(VN(G)\) |
scientific article; zbMATH DE number 1626792 |
Statements
30 July 2001
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locally compact group
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Fourier algebra
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von Neumann algebra
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\(X\)-spectral set
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\(X\)-Ditkin set
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0.88058585
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0.87371254
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0.86747897
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0.8673273
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0.86701316
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0.8635497
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Spectral synthesis for \(A(G)\) and subspaces of \(VN(G)\) (English)
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The authors consider a locally compact group \(G\), its Fourier algebra \(A(G)\) and \(VN(G)\), the von Neumann algebra generated by the left regular representation of \(G\).NEWLINENEWLINENEWLINEThey introduce the notion of \(X\)-spectral set and \(X\)-Ditkin set when \(X\) is an \(A(G)\)-invariant linear subspace of \(VN(G)\), and prove a unified approach to both spectral and Ditkin sets and their local variants. Next, they establish results on unions of \(X\)-spectral sets and \(X\)-Ditkin sets, and an injection theorem for \(X\)-spectral sets.
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