Fredholm Operators and the Essential Spectrum

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. We first give a complete treatment of Fredholm operators. Most of the results are found in the literature [4, but we have been able to substantially simplify proofs in sev eral instances. The deepest theorem we make use of is the closed graph theorem. We are able to avoid completely the concept of the opening between two subspaces.