It is a well-known result of I.C. Gohberg, M.G. Krein and T. Kato that if T is a semi-Fredholm operator between Banach spaces and P a bounded operator of norm small enough, or a compact operator, then T+P is a semi-Fredholm operator with the same index as T. This thesis is concerned with extensions of this result to more general locally made of suitably defined small bounded or precompact perturbations or Φ₊ and Φ₋ -operators. The results obtained apply in particular to Frechet spaces and effectively extend the theorems of I.C. Gohberg, M.G. Krein and T. Kata as well as several or Ju.M. Vladimirski. Duality is shown to be a convenient tool to prove many or these results. Some applications are also given.

Doctor of Philosophy (PhD)