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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Tauberian operators on Banach spaces


Authors: Nigel Kalton and Albert Wilansky
Journal: Proc. Amer. Math. Soc. 57 (1976), 251-255
MSC: Primary 47B05; Secondary 47B30
DOI: https://doi.org/10.1090/S0002-9939-1976-0473896-1
MathSciNet review: 0473896
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Abstract: A Tauberian operator: $ E \to F$ (Banach spaces) is one which satisfies $ T''g \in F,g \in E''$ imply $ g \in E$. The action of such operators and their pre-images on compact sets is studied in order to compare ``Tauberian'' with ``weakly compact", an opposite property. Properties related to range closed are introduced which force operators with Tauberian-like properties to be Tauberian. Classes of spaces appear for which Tauberian is equivalent to semi-Fredholm. One example of this is the historical reason for the definition of these operators.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0473896-1
Keywords: Tauberian, operators, Banach space
Article copyright: © Copyright 1976 American Mathematical Society