On perturbation of operators with complemented range (Q1063842)
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scientific article; zbMATH DE number 3917046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On perturbation of operators with complemented range |
scientific article; zbMATH DE number 3917046 |
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On perturbation of operators with complemented range (English)
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1984
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It is shown that if A:\(X\to Y\) is a continuous linear operator which is bounded below and has a complemented range, then for any compact operator T:\(X\to Y\) the range of AT is a closed complemented subspace of Y. Some extensions of this result and remarks concerning other generalizations are also given.
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continuous linear operator
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bounded below
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complemented range
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compact operator
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closed complemented subspace
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