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General Preservers of Quasi-Commutativity
Published online by Cambridge University Press: 20 November 2018
Abstract
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
$\Phi :{{M}_{n}}\to {{M}_{n}}$ which preserve quasi-commutativity in both directions.
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- Copyright © Canadian Mathematical Society 2010
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