Abstract view
General Preservers of QuasiCommutativity


Published:20100520
Printed: Aug 2010
Gregor Dolinar,
Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
Bojan Kuzma,
Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia
Abstract
Let ${ M}_n$ be the algebra of all $n \times n$ matrices over $\mathbb{C}$. We say that $A, B \in { M}_n$ quasicommute 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 quasicommutativity in both directions.