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Gossez’s skew linear map and its pathological maximally monotone multifunctions


Author: Stephen Simons
Journal: Proc. Amer. Math. Soc. 147 (2019), 4355-4361
MSC (2010): Primary 47H05; Secondary 47N10, 46A20, 46A22
DOI: https://doi.org/10.1090/proc/14547
Published electronically: April 18, 2019
MathSciNet review: 4002547
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Abstract: In this note, we give a generalization of Gossez’s example of a maximally monotone multifunction such that the closure of its range is not convex, using more elementary techniques than in Gossez’s original papers. We also discuss some new properties of Gossez’s skew linear operator and its adjoint.


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Additional Information

Stephen Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
MR Author ID: 189831
Email: stesim38@gmail.com

Keywords: Skew linear operator, maximal monotonicity, duality map
Received by editor(s): December 18, 2018
Received by editor(s) in revised form: January 14, 2019
Published electronically: April 18, 2019
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2019 American Mathematical Society