Veselý, Libor Some new results on accretive multivalued operators. (English) Zbl 0665.47036 Commentat. Math. Univ. Carol. 30, No. 1, 45-55 (1989). Let A be a multivalued accretive operator on a separable Banach space. Then the set of all points in a domain D(A) of A, at which A is not norm continuous, forms a first category set. If an accretive operator A on a general Banach space admits an extension which is norm-weak upper semicontinuous on int D(A), then A is norm continuous on a residual subset of int D(A). As a consequence we obtain generic continuity on int D(A) for any accretive operator on a reflexive Fréchet smooth Banach space. Each maximal accretive operator on a Banach space X has convex values iff the norm on X is Gâteaux smooth. An analogous necessary and sufficient condition for weak closedness of values of any maximal accretive operator is given, too. MSC: 47H06 Nonlinear accretive operators, dissipative operators, etc. 46B20 Geometry and structure of normed linear spaces Keywords:geometry of Banach space; \(\sigma\)-porous sets; multivalued accretive operator; extension which is norm-weak upper semicontinuous; reflexive Fréchet smooth Banach space; weak closedness of values of any maximal accretive operator PDFBibTeX XMLCite \textit{L. Veselý}, Commentat. Math. Univ. Carol. 30, No. 1, 45--55 (1989; Zbl 0665.47036) Full Text: EuDML