Ebook: Tauberian 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)

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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.

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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.

Content:
Front Matter....Pages i-xii
The origins of tauberian operators....Pages 1-7
Tauberian operators. Basic properties....Pages 9-33
Duality and examples of tauberian operators....Pages 35-71
Tauberian operators on spaces of integrable functions....Pages 73-91
Some applications....Pages 93-120
Tauberian-like classes of operators....Pages 121-190
Back Matter....Pages 191-245

---

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.

Content:
Front Matter....Pages i-xii
The origins of tauberian operators....Pages 1-7
Tauberian operators. Basic properties....Pages 9-33
Duality and examples of tauberian operators....Pages 35-71
Tauberian operators on spaces of integrable functions....Pages 73-91
Some applications....Pages 93-120
Tauberian-like classes of operators....Pages 121-190
Back Matter....Pages 191-245
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