Bidual characterization of weakly compact operators
= Bidual characterization of weakly compact operators
{title2=$T^{**}(X^{**})\subseteq J_YY$}
A <bounded linear operator> $T:X\to Y$ between <Banach spaces> is a <weakly compact operator> exactly when its second adjoint takes values in the canonical copy of $Y$ inside $Y^{**}$. The <Goldstine theorem> proves necessity; the <Banach-Alaoglu theorem>, continuity of the second adjoint, and the <Mazur theorem> prove sufficiency.