On Monotone linear relations and the sum problem in Banach spaces

On Monotone linear relations and the sum problem in Banach spaces

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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...

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Main Author: Yao, Liangjin
Language:English
Published: University of British Columbia 2012
Online Access:http://hdl.handle.net/2429/39970
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-BVAU.2429-399702014-03-26T03:38:30Z On Monotone linear relations and the sum problem in Banach spaces Yao, Liangjin 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. 2012-01-10T18:03:41Z 2012-01-10T18:03:41Z 2011 2012-01-10 2012-05 Electronic Thesis or Dissertation http://hdl.handle.net/2429/39970 eng University of British Columbia
collection NDLTD
language English
sources NDLTD
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.
author Yao, Liangjin
spellingShingle Yao, Liangjin
On Monotone linear relations and the sum problem in Banach spaces
author_facet Yao, Liangjin
author_sort Yao, Liangjin
title On Monotone linear relations and the sum problem in Banach spaces
title_short On Monotone linear relations and the sum problem in Banach spaces
title_full On Monotone linear relations and the sum problem in Banach spaces
title_fullStr On Monotone linear relations and the sum problem in Banach spaces
title_full_unstemmed On Monotone linear relations and the sum problem in Banach spaces
title_sort on monotone linear relations and the sum problem in banach spaces
publisher University of British Columbia
publishDate 2012
url http://hdl.handle.net/2429/39970
work_keys_str_mv AT yaoliangjin onmonotonelinearrelationsandthesumprobleminbanachspaces
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