Connectedness of the automorphism group of a nuclear Frechet space with a basis (Q759959)
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scientific article; zbMATH DE number 3883005
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connectedness of the automorphism group of a nuclear Frechet space with a basis |
scientific article; zbMATH DE number 3883005 |
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Connectedness of the automorphism group of a nuclear Frechet space with a basis (English)
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1984
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Let X be a nuclear Fréchet space with basis, which has a continuous norm. The following result is proved: The group \(GL(X)\) is linearly connected. For each operator \(T\in {\mathcal L}(X,X)\) there exists a path \(F(T,\tau)\) from T to the identity operator, such that \(F(T,\tau)\in GL(X)\), for \(\tau\in [0,1)\). \(GL(X)\) is everywhere dense in \({\mathcal L}_ b(X,X).\)
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nuclear Fréchet space with basis
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continuous norm
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