From the reviews:

“Tauberian operators were introduced by Kalton and Wilanski in 1976 as an abstract counterpart of some operators associated to conservative summability matrices. … The book present in a clear and unified way the basic properties of tauberian operators and their applications in functional analysis scattered throughout the literature. … is addressed to graduate students and researchers in functional analysis and operator theory, but it can be used also as a basic text for advanced graduate courses.” (V. Anisiu, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)

“The monograph under review contains the first comprehensive exposition of properties and applications of Tauberian and co-Tauberian operators, as well as of those of operators belonging to various related classes. … This monograph provides a careful unified account of ongoing research, and it is a welcome addition to the research literature on the qualitative theory of operators on Banach spaces. It is aimed at graduate students and researchers in operator theory and Banach spaces.” (Hans-Olav Tylli, Mathematical Reviews, Issue 2011 e)