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Banach Algebras

  • Ronald G. Douglas
Part of the Graduate Texts in Mathematics book series (GTM, volume 179)

Abstract

In Chapter 1 we showed thatC(X)is a Banach space and that every Banach space is, in fact, isomorphic to a subspace of someC(X).In addition to being a linear spaceC(X)is also an algebra and multiplication is continuous in the norm topology. In this chapter we studyC(X)as a Banach algebra and show thatC(X)is a “universal” commutative Banach algebra in a sense which we will later make precise. We shall indicate the usefulness and power of this result in some examples.

Keywords

Banach Algebra Division Algebra Invertible Element Function Algebra Compact Hausdorff Space 
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 Science+Business Media New York 1998

Authors and Affiliations

  • Ronald G. Douglas
    • 1
  1. 1.Department of MathematicsTexas A & M UniversityCollege StationUSA

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