Linear Continuous Operators

Linear continuous operators constitute one of the most important and well studied classes of mappings of linear normed spaces. In this chapter, we present the elementary theory of such operators. Linear continuous functionals, i.e., the mappings E → K studied in the previous chapter, are a particular case of linear continuous operators. It is clear that some properties of linear continuous operators coincide with the corresponding properties of linear functionals. Linear mappings of finite-dimensional spaces studied in linear algebra are another important particular case of these operators. Many notions and results in the theory of linear continuous operators are generalizations of the corresponding facts from linear algebra. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.