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