Geodesic
Stability of commuting maps and Lie maps
J. Alaminos1 ; J. Extremera1 ; Š. Špenko2 ; A. R. Villena1
1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
2 Institute of Mathematics, Physics, and Mechanics Ljubljana, Slovenia
Studia Mathematica, Tome 213 (2012) no. 1, pp. 25-48

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm213-1-3
Keywords: ultraprime banach algebra prove each approximately commuting continuous linear quadratic map near actual commuting continuous linear resp quadratic map furthermore analysis study close approximate lie isomorphisms approximate lie derivations actual lie isomorphisms lie derivations respectively

J. Alaminos 1 ; J. Extremera 1 ; Š. Špenko 2 ; A. R. Villena 1

1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
2 Institute of Mathematics, Physics, and Mechanics Ljubljana, Slovenia 
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J. Alaminos; J. Extremera; Š. Špenko; A. R. Villena. Stability of commuting maps and Lie maps. Studia Mathematica, Tome 213 (2012) no. 1, pp. 25-48. doi: 10.4064/sm213-1-3

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