Fréchet algebras generated by certain of their elements (Q1895275)
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scientific article; zbMATH DE number 785304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fréchet algebras generated by certain of their elements |
scientific article; zbMATH DE number 785304 |
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Fréchet algebras generated by certain of their elements (English)
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17 December 1995
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Summary: We consider \(F\)-algebras \(A\) that are generated by elements of the form \(z\), \((z- \lambda_1 e)^{-1}, \dots, (z- \lambda_N e)^{-1}\), where \(e\) is the identity. If \(A\) has no topological divisors of zero we show that \(A\) is isomorphic to \( H(\Omega)\), where \(\Omega\) is a finitely connected region. We also study \(F\)-algebras in which \(\{e, z, z^{-1}, z^2, z^{-2}, \dots\}\) is a basis.
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Fréchet algebras
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algebras of holomorphic functions
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Runge's theorem
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\(F\)-algebras
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topological divisors of zero
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