Banach Space Complexes

the long version

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 will be of interest to graduate students and specialists in functional analysis, operator theory, integral transforms, operational calculus, partial differential equations and several complex variables.