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Asplund Decompositions of Monotone Operators

Borwein, Jonathan M. (2007) Asplund Decompositions of Monotone Operators. ESAIM: Proceedings, Alain Pietrus & Michel H. Geoffroy, Editors, Control, Set-Valued Analysis and Applications.

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    Abstract

    This paper is an extended version of my talk given at the associated 2004 conference in Guadeloupe. Further related matter can be found in [4]. In a largely forgotten 1968–1970 paper, Edgar Asplund, inter alia, provided a very provocative decomposition of a maximal monotone operator as the sum of a subgradient and an acyclic (“skew”) part. In part, this forgetting is Asplund’s fault. Titles of papers really do matter ! I intend to motivate revisiting Asplund’s work on the 30th anniversary of his death, by asking how much we know about convex subgradients or monotone operators? For example, is a (bounded) linear mapping monotone iff its adjoint is? I shall then review monotonicity theory in non-reflexive spaces before presenting a modern version of an extension of one of Asplund’s decomposition results. I’ll finish with some applications and extensions and pose some hard conjectures such as all monotone pathologies are realizable with ‘skew’ mappings.

    Item Type: Book
    Additional Information: pubdom TRUE
    Subjects: 46-xx Functional analysis > 46Txx Nonlinear functional analysis
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 02 Aug 2005
    Last Modified: 26 Feb 2015 21:12
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/299

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