The concept of unbounded Fredholm operators on Hilbert -modules over an arbitrary -algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert -modules over -algebras of compact operators. In the framework of Hilbert -modules over -algebras of compact operators, the index of an unbounded Fredholm operator and the index of its bounded transform are the same.
"The Atkinson Theorem in Hilbert -Modules over -Algebras of Compact Operators." Abstr. Appl. Anal. 2007 1 - 7, 2007. https://doi.org/10.1155/2007/53060