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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
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] H. H. Bauschke, Projection algorithms and monotone operators, http://summit.sfu.ca
    /item/7015.
  • [2] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original; Allyn and Bacon Series in Advanced Mathematics. MR 0478089
  • [3] Jean-Pierre Gossez, Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs, J. Math. Anal. Appl. 34 (1971), 371-395 (French). MR 0313890, https://doi.org/10.1016/0022-247X(71)90119-3
  • [4] Jean-Pierre Gossez, On the range of a coercive maximal monotone operator in a nonreflexive Banach space, Proc. Amer. Math. Soc. 35 (1972), 88-92. MR 0298492, https://doi.org/10.2307/2038446
  • [5] Jean-Pierre Gossez, On a convexity property of the range of a maximal monotone operator, Proc. Amer. Math. Soc. 55 (1976), no. 2, 359-360. MR 0397485, https://doi.org/10.2307/2041724
  • [6] Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157

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Additional Information

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

DOI: https://doi.org/10.1090/proc/14547
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