On Jordan all-derivable points of \(\mathcal B(\mathcal H)\) (Q999775)
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scientific article; zbMATH DE number 5505603
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Jordan all-derivable points of \(\mathcal B(\mathcal H)\) |
scientific article; zbMATH DE number 5505603 |
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On Jordan all-derivable points of \(\mathcal B(\mathcal H)\) (English)
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10 February 2009
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Let \(H\) be an infinite-dimensional Hilbert space. It is shown that a linear map \(\delta:B(H)\to B(H)\) satisfying \(\delta(A)A + A\delta(A) = A\delta(I)A\) whenever \(A^2 =0\) is a generalized derivation. Similarly, a linear map \(\delta:B(H)\to B(H)\) is a derivation provided that \(\delta(I) = \delta(A)A + A\delta(A)\) whenever \(A^2=I\) (here, \(H\) need not be infinite-dimensional).
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Jordan all-derivable point
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generalized Jordan all-derivable point
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Jordan derivable map
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generalized Jordan derivable map
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derivation
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generalized derivation
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