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Faces and support functions for the values of maximal monotone operators. (English) Zbl 07246144

Summary: 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 reflexive and locally uniformly convex real Banach spaces with locally uniformly convex duals, or their domains have nonempty interiors on 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.

MSC:

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