Phelps, R. R. Lectures on maximal monotone operators. (English) Zbl 0932.47040 Extr. Math. 12, No. 3, 193-230 (1997). 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. Reviewer: Vassil Angelov (Sofia) Cited in 27 Documents MSC: 47H04 Set-valued operators 47H05 Monotone operators and generalizations 58C20 Differentiation theory (Gateaux, FrĂ©chet, etc.) on manifolds 49J52 Nonsmooth analysis Keywords:non-reflexive Banach space; maximal monotone operators; subdifferentials of convex functions; type \((D)\); locally maximal monotone operators PDFBibTeX XMLCite \textit{R. R. Phelps}, Extr. Math. 12, No. 3, 193--230 (1997; Zbl 0932.47040) Full Text: arXiv EuDML