On the nilpotent generalized derivations with closed range in Banach spaces (Q1823440)
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scientific article; zbMATH DE number 4115341
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nilpotent generalized derivations with closed range in Banach spaces |
scientific article; zbMATH DE number 4115341 |
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On the nilpotent generalized derivations with closed range in Banach spaces (English)
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1989
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Given complex Banach spaces X and Y, the generalized derivation \({\mathcal T}_{AB}\), \(A\in B(X)\) and \(B\in B(Y)\), is defined by \({\mathcal T}_{AB}S=AS-SB\) for \(S\in B(Y,X)\). The author considers the problem of finding conditions under which the range of \({\mathcal T}_{AB}\) is norm closed. Here a partial answer for nilpotent A and B is given.
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derivations with closed range in Banach spaces
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nilpotent
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operators
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generalized derivation
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