- Title
- Construction of pathological maximally monotone operators on non-reflexive Banach spaces
- Creator
- Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
- Relation
- Set Valued and Variational Analysis Vol. 20, Issue 3, p. 387-415
- Publisher Link
- http://dx.doi.org/10.1007/s11228-012-0209-0
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2012
- Description
- 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 ensuremathJ or its dual ensuremathJ*, or c 0 or its dual ℓ¹, admits a non type (D) operator. The existence of non type (D) operators in spaces containing ℓ¹ or c 0 has been proved recently by Bueno and Svaiter.
- Subject
- adjoint; BC–function; operator of type (NI); partial inf-convolution; Schauder basis; set-valued operator; shrinking basis; skew operator; space of type (D); uniqueness of extensions; subdifferential operator; primary 47A06; Fitzpatrick function; 47H05; secondary 47B65; 47N10; 90C25; James space; linear relation; maximally monotone operator; monotone operator; multifunction; operator of type (BR); operator of type (D)
- Identifier
- http://hdl.handle.net/1959.13/939957
- Identifier
- uon:12910
- Identifier
- ISSN:1877-0533
- Rights
- The final publication is available at www.springerlink.com
- Language
- eng
- Full Text
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