Abstract
A bounded linear operatorT:X→Y(Banach spaces) is defined to be Tauberian provided whenever {xn}⊂Xis bounded and {T(xn)}⊂Yis weakly convergent, then {xn} has a weakly convergent subsequence. Hence, they appear as opposite to weakly compact operators. In 1991 a Tauberian operatorTbetween separable Banach spaces was found such that its second conjugateT** is not Tauberian. ThoughT** might not be Tauberian, in this paper we prove that it satisfies the following property whenXis separable: whenever {x*n*}⊂X** is bounded and {T**(x*n*)}⊂Y** is weakly convergent, then {x*n*} has aw*-convergent subsequence. Other properties ofT** are proved and the nonseparable case is also studied.
Published Version
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