Sums of Monotone Operators
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The sum of two monotone operators is monotone. However, maximal monotonicity of the sum of two maximally monotone operators is not automatic and requires additional assumptions. In this chapter, we provide flexible sufficient conditions for maximality. Under additional assumptions, conclusions can be drawn about the range of the sum, which is important for deriving surjectivity results. We also consider the parallel sum of two set-valued operators.
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