On the duality theorem of bounded S-decomposable operators

A class of linear operators, more general than that of the decomposable operators, here referred to as S-decomposable operators, was introduced in 10]. It was shown in 11] that the dual of an S-decomposable operator was again S-decomposable. Our main result, in this paper, is the converse implication, namely, if the dual $\text{T1}$ of a bounded linear operator T is S-decomposable then T is S-decomposable.