
arXiv: 1412.6195
We give, for general Banach spaces, a characterization of the sequential lower limit of maximal monotone operators of type (D) and prove its representability. As a consequence, using a recent extension of the Moreau-Yosida regularization for type (D) operators, we extend to general Banach spaces the definitions of the variational sum of monotone operators and the variational composition of monotone operators with continuous linear mappings, and we prove that both operators are representable.
lower limits, Moreau-Yosida regularization, monotone set-valued operators, variational sum, Functional Analysis (math.FA), Banach spaces, variational composition, Optimization and Control (math.OC), Optimization and Control, FOS: Mathematics, 46H05, 49J52, 46N10, Set-valued operators, Monotone operators and generalizations, Functional Analysis, Set-valued and variational analysis
lower limits, Moreau-Yosida regularization, monotone set-valued operators, variational sum, Functional Analysis (math.FA), Banach spaces, variational composition, Optimization and Control (math.OC), Optimization and Control, FOS: Mathematics, 46H05, 49J52, 46N10, Set-valued operators, Monotone operators and generalizations, Functional Analysis, Set-valued and variational analysis
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