Linear Operators in Banach Spaces

Abstract

In this chapter we present a brief introduction to basic concepts of Operator Theory, and some relevant classes of operators are introduced to what follows thereafter. The most explored Banach spaces in the text are the spaces $E=(C^{k}(K;\mathbb {R}^{m}),\mid \mid f\mid \mid _{C^{k}})$, as defined in Appendix A. Eventually, the spaces $L^{p}$ are used, but we avoid them since more care is required with the analysis. Our larger goal is to study the differentiable maps; for this purpose the spaces $C^{k}$ are enough.