A+ CATEGORY SCIENTIFIC UNIT

Stability of commuting maps and Lie maps

Volume 213 / 2012

J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena 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.

Authors

  • J. AlaminosDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • J. ExtremeraDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • Š. ŠpenkoInstitute of Mathematics, Physics, and Mechanics
    Ljubljana, Slovenia
    e-mail
  • A. R. VillenaDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail

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