Abstract and Applied Analysis
Volume 2007 (2007), Article ID 53060, 7 pages
The Atkinson Theorem in Hilbert -Modules over -Algebras of Compact Operators
1Department of Mathematics, Ferdowsi University, Mashhad 91775, Iran
2Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University, Mashhad 91775, Iran
Received 13 August 2007; Accepted 4 November 2007
Academic Editor: Victor G. Zvyagin
Copyright © 2007 A. Niknam and K. Sharifi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.