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COMPOUND-COMMUTING ADDITIVE MAPS ON MATRIX SPACES

  • Chooi, Wai Leong (INSTITUTE OF MATHEMATICAL SCIENCES UNIVERSITY OF MALAYA)
  • Received : 2009.04.10
  • Accepted : 2010.05.19
  • Published : 2011.01.01

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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Cited by

  1. Nonstandard rank-one nonincreasing maps on symmetric matrices pp.1563-5139, 2017, https://doi.org/10.1080/03081087.2017.1419456