On Weakly Conditionally Compact Tauberian Operators

Tauberian operators appeared in a problem of summability and were studied by Kalton and Wilansky and other authors. Moreover they have received some attention because they form a broader class than that of isomorphisms (into) but yet they preserve some isomorphic properties of Banach spaces.

The aim of this paper is to generalize the definition of tauberian operators by using the notion of weakly conditionally compact set.

As consequence, some properties of the classic tauberian operators have counterparts in this new context, taking into account that the roll played by the reflexivity in the tauberian operators is played in the case of weakly conditionally compact tauberian operators by the fact of not containing copies of l¹.