On stability of index of Fredholm complexes on the C*-algebra

Abstract

This article deals with the index of Fredholm complexes of Λ-operators of the Hilbert Λ-modulus on C*-algebra. For this class of operators necessary and sufficient conditions in order to be a Fredholm, are obtained. Based on these results, a notion of Fredholm complex and its index is introduced. For this index, a stability theorem related to various perturbations is proved. In the second part of the article, a completation of a semigroup Fredholm complexes is analysed. It is proved that the group K _G (X, Λ) is the completation of G − Λ-fibration of the above group on the compact space X.

Keywords:

• Fredholm complex
• Λ-operators on C*-algebra
• perturbation
• index

AMS 2000 Subject Classification:

• 47C15
• 47A53
• 55N15

Acknowledgements

The author would like to thank Professor Alemdar Hasanoglu for various suggestions which improve the manuscript.