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

Convolution 

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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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