Restrictions of unbounded continuous linear operators on Fréchet spaces (Q1066412)
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scientific article; zbMATH DE number 3925540
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Restrictions of unbounded continuous linear operators on Fréchet spaces |
scientific article; zbMATH DE number 3925540 |
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Restrictions of unbounded continuous linear operators on Fréchet spaces (English)
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1986
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It is proved that if E is a Fréchet space, F a closed subspace of a Fréchet space \(F_ 1\) which has a basis and admits a continuous norm and \(T: E\to F\) is a continuous unbounded linear operator, then there is an infinite-dimensional closed nuclear subspace G of E which has a basis such that the restriction of T to G is an isomorphism onto T(G). In the proof, a modification of a result of Bessaga, Pelczynski and Rolewicz, which was employed to construct a nuclear subspace of a Fréchet space is used.
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basic sequences
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continuous norm
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continuous unbounded linear operator
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nuclear subspace of a Fréchet space
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