The Atkinson Theorem in Hilbert $C^*$-Modules over $C^*$-Algebras of Compact Operators
A. Niknam and K. Sharifi
Source: Abstr. Appl. Anal. Volume 2007 (2007), 7 pages.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1204126608
Digital Object Identifier: doi:10.1155/2007/53060
Mathematical Reviews number (MathSciNet):
MR2375449
Abstract and Applied Analysis