The Atkinson Theorem in Hilbert C * -Modules over C * -Algebras of Compact Operators

Abstract

The concept of unbounded Fredholm operators on Hilbert $C^{*}$-modules over an arbitrary $C^{*}$-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert $C^{*}$-modules over $C^{*}$-algebras of compact operators. In the framework of Hilbert $C^{*}$-modules over $C^{*}$-algebras of compact operators, the index of an unbounded Fredholm operator and the index of its bounded transform are the same.