Representation Theory

  • Bernard Aupetit
Part of the Universitext book series (UTX)


Let A be a Banach algebra. A linear functional ϰ on A is called a character of A if it is multiplicative and not identical to 0 on A. This last condition is equivalent to saying that ϰ(1) = 1 because ϰ(x) = ϰ(x)ϰ(1). If ϰ is a character of A it is easy to verify that ϰ(x)∈ Sp(x), for all xA, because (x - ϰ(x)1)y = y(x - ϰ(x)1) = 1 leads to an absurdity. Consequently \(|\chi (x)| \leqslant \rho (x) \leqslant \parallel x\parallel\) so a character is continuous and of norm one.


Banach Space Irreducible Representation Representation Theory Spectral Theory Banach Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Bernard Aupetit
    • 1
  1. 1.Départment de Mathématiques et StatistiqueUniversité LavalQuébecCanada

Personalised recommendations