Monotone Linear Relations: Maximality and Fitzpatrick Functions

Abstract

We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick family is obtained. We also answer one of Simons problems by showing that if a maximal monotone operator has a convex graph, then this graph must actually be affine.

References in corpus (3)

• The Sum Theorem for Linear Maximal Monotone Operators
• Maximal monotone operators with a unique extension to the bidual
• Linear Monotone Subspaces of Locally Convex Spaces

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