Derivable mappings at unit operator on nest algebras (Q875025)
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scientific article; zbMATH DE number 5141646
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derivable mappings at unit operator on nest algebras |
scientific article; zbMATH DE number 5141646 |
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Derivable mappings at unit operator on nest algebras (English)
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10 April 2007
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In this paper, the following result is proved. Let \(H\) be a complex, separable Hilbert space and let \(N\) be a complete nest on~\(H\). Let \(\varphi: N\to N\) be a strong operator topology continuous linear mapping. Then \(\varphi\) is a derivable mapping at \(1\), that is, \[ \varphi(ST)=\varphi(S)T+S\varphi(T)\quad(S,T\in N,\;ST=1) \] if and only if \(\varphi\) is an inner derivation implemented by an operator in~\(B(H)\). The proof is largely computational.
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operator algebra
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derivable mapping
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inner derivation
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