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Construction of Pathological Maximally Monotone Operators on Non-reflexive Banach Spaces

Bauschke, Heinz H. and Borwein, Jonathan M. and Wang, Xianfu and Yao, Liangjin (2012) Construction of Pathological Maximally Monotone Operators on Non-reflexive Banach Spaces. Set-Valued Var. Anal., 20 (3). pp. 387-415.

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    Abstract

    In this paper, we construct maximally monotone operators that are not of Gossez’s dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brønsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC–functions will not always be a BC–function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce — in a uniform fashion — that every Banach space which contains an isomorphic copy of the James space J or its dual $J^\ast,$ or $c_0$ or its dual $l^1,$ admits a non type (D) operator. The existence of non type (D) operators in spaces containing $l^1$ or $c_0$ has been proved recently by Bueno and Svaiter.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 03 Jan 2015 21:13
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1090

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