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On Monotone linear relations and the sum problem in Banach spaces

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Title: On Monotone linear relations and the sum problem in Banach spaces
Author: Yao, Liangjin
Degree Doctor of Philosophy - PhD
Program Mathematics
Copyright Date: 2011
Publicly Available in cIRcle 2012-01-10
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.
URI: http://hdl.handle.net/2429/39970
Scholarly Level: Graduate

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