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This book offers a systematic approach to the study of those properties of Banach space complexes that are stable under certain perturbations. The stability of the index under small or compact perturbations is presented within the context of (semi-)Fredholm complexes. Various invariants and other properties are also considered. This raises certain problems requiring further study of more general Fredholm-type objects. Some of the results are new. Applications in several variables spectral theory and in other related fields are also given. Audience: This largely self-contained book...

The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ..., where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP: Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S: X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X Y ..... O. The already existing Fredholm...