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Some new results on accretive multivalued operators. (English) Zbl 0665.47036
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.
47H06 Nonlinear accretive operators, dissipative operators, etc.
46B20 Geometry and structure of normed linear spaces
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