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Representation Theory

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

Abstract

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.

Keywords

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.

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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

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

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