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1. CJM 2010 (vol 62 pp. 758)
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General Preservers of Quasi-Commutativity Let ${ M}_n$ be the algebra of all $n \times n$ matrices over $\mathbb{C}$. We say that $A, B \in { M}_n$ quasi-commute if there exists a nonzero $\xi \in \mathbb{C}$ such that $AB = \xi BA$. In the paper we classify bijective not necessarily linear maps $\Phi \colon M_n \to M_n$ which preserve quasi-commutativity in both directions.
Keywords:general preservers, matrix algebra, quasi-commutativity Categories:15A04, 15A27, 06A99 |