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