Journal of Convex Analysis 29 (2022), No. 3, 789--794
Copyright Heldermann Verlag 2022
On the Convexity of the Closure of the Domain/Range of a Maximally Monotone Operator
Maria E. Verona
Dept. of Mathematics, University of Southern California, Los Angeles, U.S.A.
verona@usc.edu
Andrei Verona
Dept. of Mathematics, California State University, Los Angeles, U.S.A.
averona10@yahoo.com
We prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain/range and is maximal.
Keywords: Monotone operator, maximally monotone operator, Fitzpatrick function, Simons' conditions, type (FP).
MSC: 47H05; 47A65.
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