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Lectures on maximal monotone operators. (English) Zbl 0932.47040

These lectures are profound investigations devoted to the properties of maximal monotone operators in arbitrary (non-reflexive) real Banach spaces. In Section 1, the author defines maximal monotone operators and proves some of their main elementary properties. Section 2 is devoted to the prototypical class of subdifferentials of convex functions. Gossez’s subclass of monotone operators of type \((D)\) is examined in Section 3 and Section 4 gives a brief treatment of another subclass, the locally maximal monotone operators. He has attempted to keep the exposition selfcontained using only standard tools of elementary functional analysis.

MSC:

47H04 Set-valued operators
47H05 Monotone operators and generalizations
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
49J52 Nonsmooth analysis
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