Abstract and Applied Analysis
Volume 2007 (2007), Article ID 53060, 7 pages
doi:10.1155/2007/53060

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.