Faces and Support Functions for the Values of Maximal Monotone Operators

DOI10.1007/S10957-020-01737-3arXiv1911.04892MaRDI QIDQ6329010

Publication date: 12 November 2019

Abstract: Representation formulas for faces and support functions of the values of maximal monotone operators are established in two cases: either the operators are defined on uniformly Banach spaces with uniformly convex duals, or their domains have nonempty interiors on reflexive real Banach spaces. Faces and support functions are characterized by the limit values of the minimal-norm selections of maximal monotone operators in the first case while in the second case they are represented by the limit values of any selection of maximal monotone operators. These obtained formulas are applied to study the structure of maximal monotone operators: the local unique determination from their minimal-norm selections, the local and global decompositions, and the unique determination on dense subsets of their domains.

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Set-valued maps in general topology (54C60) Set-valued operators (47H04) Linear operators on Banach algebras (47B48) Convexity of real functions of several variables, generalizations (26B25) Operator theory (47-XX)

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