Banach algebras

  • Steffen RochEmail author
  • Pedro A. Santos
  • Bernd Silbermann
Part of the Universitext book series (UTX)


Banach algebras provide a framework for many of the local principles. This chapter summarizes the material from Banach algebra theory which is needed in order to understand the following chapters. A reader who is acquainted with the basics of Banach algebras can certainly skip this chapter. On the other hand, we have tried to present the text in a (nearly) self-contained manner. Thus, all basic results are provided with a proof, whereas we have to refer to the literature for the proofs of some results which are mentioned only as an aside. This concerns in particular some results on C -algebras, which form certainly the most important subclass of Banach algebras, but which will not play a distinguished role in this text.


Maximal Ideal Banach Algebra Left Ideal Singular Integral Operator Closed Ideal 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Steffen Roch
    • 1
    Email author
  • Pedro A. Santos
    • 2
  • Bernd Silbermann
    • 3
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Instituto Superior Técnico, Departamento de MatemáticaUniversidade Técnica de LisboaLisboaPortugal
  3. 3.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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