On a characterization of linear operators (Q1917173)
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scientific article; zbMATH DE number 897185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a characterization of linear operators |
scientific article; zbMATH DE number 897185 |
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On a characterization of linear operators (English)
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4 August 1997
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Main result: Let \(X\) be a real or complex vector space and let \(B\) be a normed space. The function \(f:X\to B\) is linear if and only if the function \[ (x,y,\lambda)\mapsto f(\lambda x+y)-\lambda f(x)-f(y) \] remains bounded for large \(\lambda\). The author claims that this statement holds also if \(B\) is a locally convex topological vector space.
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linear operator bounded function
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bounded function
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locally convex topological vector space
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