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Banach algebras and uniform algebras

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Part of the Monografie Matematyczne book series (MONOGRAFIE, volume 68)

Abstract

In this chapter we present a part of the uniform algebra theory we will need, including several important algebraic constructions. Basic notations, terminology, and selected auxiliary results concerning commutative Banach algebras and uniform algebras are presented in the first two sections. The inductive and projective limits of algebras, introduced in more detail, are very convenient tools for describing the structure and revealing the hidden features of specific uniform algebras. Bourgain algebras and polynomial extensions provide powerful methods for constructing new classes of algebras. Further we discuss isomorphisms and homomorphisms between uniform algebras.

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© Birkhäuser Verlag 2006

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