Additive mappings that preserve rank one nilpotent operators. (Q1873708)
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scientific article; zbMATH DE number 1917813
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Additive mappings that preserve rank one nilpotent operators. |
scientific article; zbMATH DE number 1917813 |
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Additive mappings that preserve rank one nilpotent operators. (English)
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27 May 2003
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Let \(B(X)\) be the algebra of bounded operators on a complex infinite-dimensional Banach space \(X\) and \(F(X)\) be the subalgebra of all finite rank operators in \(B(X)\). A characterization of additive maps on \(F(X)\) which preserve rank one nilpotent operators in both directions is given. As application of this result, some additive preservers are obtained.
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additive preservers
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nilpotents
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potents
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idempotents
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rank
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