文献类型：期刊文献

英文题名：WEAK CONTINUITY OF THE NORMALIZED DUALITY MAP

作者：Xu, Hong-Kun[1,2];Kim, Tae Hwa[3];Yin, Ximing[4]

机构：[1]Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan;[2]King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia;[3]Pukyong Natl Univ, Coll Nat Sci, Dept Appl Math, Pusan 608737, South Korea;[4]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2014

卷号：15

期号：3

起止页码：595

外文期刊名：JOURNAL OF NONLINEAR AND CONVEX ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000331495900013)】；

基金：Supported in part by NSC 102-2115-M-110-001-MY3.Corresponding author and supported by Pukyong National University Research Fund (C-D-2012-0707).

语种：英文

外文关键词：Duality map; gauge; weak continuity; product space; permanence; renorm

摘要：The duality maps play a crucial role in solving nonlinear problems in the setting of Banach spaces, due to the lack of an inner product on Banach spaces. Weak continuity of duality maps is required occasionally, and even weak continuity of the normalized duality is assumed by some authors. We will show that weak continuity of the normalized duality in infinite-dimensional spaces is an inappropriate assumption as the normalized duality map of the sequential space l(p) for 1 < p < infinity fails to be weakly continuous unless p = 2. Consequently, assuming weak continuity of a generalized duality map is more appropriate in dealing with nonlinear problems in Banach spaces.