Abstract
This chapter describes weak continuity and compactness of nonlinear operators. It is known that the properties of weak continuity and compactness of a nonlinear operator F: X → Y, where X and Y are Banach spaces, play a central role in the study of nonlinear equations. Relations between these properties and the behavior of the derivative, F′, of F have been investigated for some time. The chapter introduces a topology on B(X, Y) which is much weaker than the norm topology. The chapter establishes relations between the mapping F′: X → B(X, Y), where F′ is the (linear) Gateaux derivative, and the properties of compactness and weak sequential continuity of F.
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