The closedness property and the pseudo-A-properness of accretive operators
\textit{J. R. L. Webb} [J. Math. Anal. Appl. 85, 146-152 (1982; Zbl 0477.47035)] proved a closedness property of an m-accretive operator T: D(T)\(\subset E\to E\) when E is a separable, uniformly convex Banach space with uniformly convex dual \(E^*\) to the effect that for every bounded sequence \(\{x_ n\}\subset D(T)\) with \(Tx_ n\to f\) there exists \(v\in D(T)\) such that \(Tv=f\). The paper under review gives a generalization of this result to a general multi-valued m-accretive operator, removing the hypotheses of separability and uniform convexity of the space E. It also argues about pseudo-A-properness.
uniformly convex Banach space with uniformly convex dual
scientific article; zbMATH DE number 4078092