Date of Award
1977
Degree Type
Thesis
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Supervisor
T. Husain
Abstract
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.
Recommended Citation
Chu, Lo Quang, "Perturbations of semi-Fredholm operators in locally convex topological vector spaces" (1977). Open Access Dissertations and Theses. Paper 3764.
http://digitalcommons.mcmaster.ca/opendissertations/3764