Characterizations of Tauberian and Related Operators on Banach Spaces

If E and F and Banach spaces, a bounded linear operator T: E ⇒ F is called Tauberian if whenever G ∈ E** and T**(G) ∈ F, then G ∈ E. Internal characterizations of Tauberian operators and operators having Property N in terms of their behavior on basic sequences are given. From these, other properties of Tauberian operators are derived.