Linear Operators

Linear operators have already received quite a bit of attention in this book, primarily as tools for probing the structure of normed spaces. The purpose of this chapter is to reverse that emphasis temporarily by studying linear operators between normed spaces as interesting objects in their own right, with the properties of normed spaces obtained in the first two chapters used as the tools for the study. Almost all of the attention will be on bounded linear operators, though there is also an interesting theory of unbounded ones; see, for example, Chapter 13 of [200] or Chapter VII, Section 9 of [67].