Tauberian operators were introduced to investigate a problem in summability theory from an abstract point of view. Since that introduction, they have made a deep impact on the isomorphic theory of Banach spaces. In fact, these operators havebeen useful in severalcontexts of Banachspacetheory that haveno apparent or obvious connections. For instance, they appear in the famous factorization of Davis, Figiel, Johnson and Pe lczynski 49] (henceforth the DFJP factorization), in the study of exact sequences of Banach spaces 174], in the solution of certain summabilityproblemsoftauberiantype...