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.
KeywordsMaximal Ideal Banach Algebra Left Ideal Singular Integral Operator Closed Ideal
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