On additivity of commutator preserving bijections in a matrix algebra (Q2713985)
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scientific article; zbMATH DE number 1603236
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On additivity of commutator preserving bijections in a matrix algebra |
scientific article; zbMATH DE number 1603236 |
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10 June 2001
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matrix algebra
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commutator
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bijection
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0.9177036
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0.90531766
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0.8992579
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0.8979534
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0.89770347
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On additivity of commutator preserving bijections in a matrix algebra (English)
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Let \(M_2^0\) be the set of real \(2\times 2\)-matrices with zero trace. Put \([A,B]=AB-BA\) \((A,B\in M_2^0)\). The main result of the article can be stated as follows: Let \(\varphi\) be a bijection from \(M_2^0\) onto \(M_2^0\) such that \(\varphi([A,B])=[\varphi(A),\varphi(B)]\) for all \(A,B\in M_2^0\). Then \(\varphi(A+B)=\varphi(A)+\varphi(B)\) for all \(A,B\in M_2^0\).
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