Norm-attaining property for a dual pair of Banach spaces

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• 作者：Cheuk-Yin Lee ^{cylee@math.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author} ; Chi-Wai Leung ; ^{cwleung@math.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fourier&ndash ; Stieltjes algebra ; Fourier space ; Norm-attaining property ; Simons' inequality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：556-563
• 全文大小：323 K

文摘

In this study, we introduce the norm-attaining property for a dual pair of Banach spaces. We use this property to determine a quotient Banach space as a dual space. We also apply this property to obtain another proof of the James's characterization theorem regarding the reflexivity of a separable Banach space. In addition, the norm-attaining property of a Fourier space is studied.