Tauberian Operators

This book gives a complete exposition of the theory of tauberian operators from the very basic results to the most recent advances making emphasis in its applications to Banach space theory. After describing the origins of the subject in the study of summability of series, it presents the general theory for tauberian operators on abstract Banach spaces. The main sources of examples of tauberian operators are described in detail, including the case of operators on spaces of integrable functions.