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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-3,
author = {J. Alaminos and J. Extremera and \v S. \v Spenko and A. R. Villena},
title = {Stability of commuting maps and Lie maps},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {25-48},
zbl = {1281.47022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-3}
}
J. Alaminos; J. Extremera; Š. Špenko; A. R. Villena. Stability of commuting maps and Lie maps. Studia Mathematica, Tome 209 (2012) pp. 25-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-3/