Additive maps on hermitian matrices

Abstract

Suppose is a field with proper involution and of arbitrary characteristic. Additive maps, which do not increase rank-one on hermitian matrices with entries from are classified. The result is then used to classify additive maps that do not increase minimal rank on the set of symmetric elements, relative to general involution on a matrix algebra.

Keywords:

• Involution
• Symmetric element
• Hermitian matrix
• Rank
• Additive preserver

Keywords:

• Mathematics Subject Classifications (2000): 15A04
• 15A03
• 15A57

Acknowledgement

This work was supported by grants from the Ministry of Science of Slovenia.