Introduction

Modern mathematics depends to a considerable degree upon extending the finite to the infinite. In this regard, the modern subject of Functional Analysis can be thought of as the infinite dimensional version of Linear Algebra. There does not seem to be any inherent difficulty in extending geometric vectors and their operations of addition and the dot product to ‘infinite’ vectors. Nevertheless a naive approach encounters several apparent paradoxes and pitfalls, necessitating a more rigorous path. Functional analysis is a rich subject because it combines the topological and algebraic branches of mathematics. As in the rest of mathematics, there are two equally important streams of study, the abstract theory and the concrete examples. It is often by examples that one understands the abstract, and by the theory that one makes headway with concrete problems.