Closure Operations of Convex Sets in $$X\times X^{*}$$ and Monotone Operators

Abstract We develop a number of new results on “closure operations” based on $$s\times \text{w}^{*}$$ s × w ∗ -convergence of bounded nets for convex sets and functions on $$X\times X^{*}$$ X × X ∗ . We discuss their relevance to the study of monotone operators defined on possibly non-reflexive, real Banach spaces.