This text offers a complete exposition of the theory of tauberian operators. It describes the origins of the subject in the study of summability of series, and it covers the most recent advances, emphasizing its applications to Banach space theory.
The origins of tauberian operators.- Tauberian operators. Basic properties.- Duality and examples of tauberian operators.- Tauberian operators on spaces of integrable functions.- Some applications.- Tauberian-like classes of operators.
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)
First unified exposition of the theory of tauberian operators
Describes a wide range of applications of the topic
Self-contained and accessible for both graduate students and researchers
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