Introduction

In this monograph authors are concerned with real function algebras, which are, in particular, Banach algebras. For this reason they begin by developing the necessary theory of real Banach algebras. Another reason for developing this general theory is that in the study of real function algebras, they have to deal with some Banach algebras that are not real function algebras. This chapter introduces the relatively recently developed topic of perturbation of Banach algebras. Since then, many mathematicians have attempted to develop the theory of real function algebras along the lines of complex function algebras. The authors soon establish that the class of real function algebras includes that of complex function algebras.