We establish the semi-Fredholm theory on Hilbert -modules as a continuation of Fredholm theory on Hilbert -modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert -module, and we prove that these semi-Fredholm operators are those that are one-sided invertible modulo compact operators, that the set of proper semi-Fredholm operators is open, and many other results that generalize their classical counterparts.
"Semi-Fredholm theory on Hilbert -modules." Banach J. Math. Anal. 13 (4) 989 - 1016, October 2019. https://doi.org/10.1215/17358787-2019-0022