Tauberian operators on Banach spaces

Kalton, Nigel; Wilansky, Albert

doi:10.1090/S0002-9939-1976-0473896-1

Tauberian operators on Banach spaces
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by Nigel Kalton and Albert Wilansky

Proc. Amer. Math. Soc. 57 (1976), 251-255

DOI: https://doi.org/10.1090/S0002-9939-1976-0473896-1

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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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