In a nonreflexive space the subdifferential is not onto
This paper extends the theorem of R. C. James that a Banach space X is reflexive if and only if each continuous linear functional attains its supremum on the unit ball. The result is that for \(\phi\) a lower semicontinuous convex function on X with the interior of its domain nonempty, \(\partial \phi\) is surjective iff for all g in \(X^*\), the function g-\(\phi\) is bounded above and X is reflexive. The paper asks: If \(A:X\to X^*\) is a monotone operator with \(R(A)=X^*\) and int D(A)\(\neq \Phi\), must X be reflexive?
scientific article; zbMATH DE number 3877796