Characterizations of Tauberian and related operators on Banach spaces (Q1310865)

If \(E\) and \(F\) are Banach spaces, a bounded linear operator \(T: E\to F\) is called Tauberian if whenever \(G\in E^{**}\) and \(T^{**}(G)\in F\), then \(G\in E\). The author gives internal characterizations of Tauberian operators and operators having Property N in terms of their behavior on basic sequences. From these, other properties of Tauberian operators are derived.