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On Monotone linear relations and the sum problem in Banach spaces Yao, Liangjin
Abstract
We study monotone operators in general Banach spaces. Properties and characterizations of monotone linear relations are presented. We focus on the "sum problem" which is the most famous open problem in Monotone Operator Theory, and we provide a powerful sufficient condition for the sum problem. We work on classical types of maximally monotone operators and provide affirmative answers to several open problems posed by Phelps and by Simons. Borwein-Wiersma decomposition and Asplund decomposition of maximally monotone operators are also studied.
Item Metadata
| Title |
On Monotone linear relations and the sum problem in Banach spaces
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2011
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| Description |
We study monotone operators in general Banach spaces. Properties and characterizations of monotone linear relations are presented.
We focus on the "sum problem" which is the most famous open problem in Monotone Operator Theory, and we provide a powerful sufficient condition for the sum problem. We work on classical types of maximally monotone operators and provide affirmative answers to several open problems posed by Phelps and by Simons. Borwein-Wiersma decomposition and Asplund decomposition of
maximally monotone operators are also studied.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2012-01-10
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0072528
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2012-05
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Attribution-NonCommercial-NoDerivatives 4.0 International