The Proof of the Inversion Mapping Theorem in a Banach Scale

Abstract

This chapter discusses the proof of the inversion mapping theorem in a Banach scale. This theorem cannot be extended, ipsis litteris, in a Banach Scale. This chapter presents a counter example. It enunciated that, using the generalized Frobenius theorem, one can obtain a "right" inversion theorem. It provides a complete proof and proves that one can obtain an inversion theorem. The classical inversion theorem in a Banach Space is a particular case of such situation.