ABSTRACT
An operator is a mathematical device that determines the way in which elements in a set are mapped to elements in another set. The simplest example of a mapping is the function f that associates each number y in R or C with a number x in R or C, respectively. This mapping is commonly designated using y = f (x) or f : x→ y. In the study of functional analysis, more general types of mappings must be considered. These include mappings between points, numbers, functions, and other abstract mathematical entities. Despite multiplicity of entities we will consider, we would like to continue our discussion using a single perspective. In order to do this, we employ operator theory, which is a major branch of functional analysis.
