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.
KeywordsBanach Algebra Division Algebra Invertible Element Function Algebra Compact Hausdorff Space
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