Commuting maps on some subsets that are not closed under addition

• Main Author: Franca, Willian V.
• Language: EN
• Published: Kent State University 2014
• Subjects: Mathematics
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=3618894

<p> The theory of commuting maps on rings and algebras is a very active research area in linear algebra, operator theory and ring theory. The aim of this work is to study commuting maps on some subsets of matrix and operator algebras which are not closed under addition. In particular, we characterize commuting maps on the sets of invertible matrices, singular matrices, and matrices of fixed rank. </p><p> As applications of our results we describe additive maps preserving additive/multiplicative commutators on some important matrix subsets. Our research in this direction is motivated by a long-standing problem posed by Herstein about the characterization of maps preserving multiplicative commutators on simple rings. </p>