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Representation Theory for C-Algebras and the Spectral Theorem

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

Abstract

Among Banach algebras there are very interesting ones called Banach algebras with involution. A mapping xx from a Banach algebra A into itself is called an involution on A if it satisfies the following properties for all x,yA and λ ∈ ℂ:
  1. (i)

    (x + y) = x + y

     
  2. (ii)

    \({{(\lambda x)}^{ \star }} = \bar{\lambda }{{x}^{ \star }},\)

     
  3. (iii)

    (xy) = yx

     
  4. (iv)

    (x) = x.

     

Keywords

Representation Theory Spectral Theory Banach Algebra Left Ideal Borel Subset 
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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