Stability of commuting maps and Lie maps
Volume 213 / 2012
Studia Mathematica 213 (2012), 25-48
MSC: Primary 47B48; Secondary 17B40, 16R60.
DOI: 10.4064/sm213-1-3
Abstract
Let $A$ be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on $A$ is near an actual commuting continuous linear (resp. quadratic) map on $A$. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
