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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.
MSC:
47H06 Nonlinear accretive operators, dissipative operators, etc.
46B20 Geometry and structure of normed linear spaces
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