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http://dx.doi.org/10.4134/JKMS.2011.48.1.083

COMPOUND-COMMUTING ADDITIVE MAPS ON MATRIX SPACES  

Chooi, Wai Leong (INSTITUTE OF MATHEMATICAL SCIENCES UNIVERSITY OF MALAYA)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 83-104 More about this Journal
Abstract
In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.
Keywords
rank; compound matrix; compound-commuting additive map; rank-one nonincreasing additive map;
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