Exposed 2-Homogeneous Polynomials on the two-Dimensional Real Predual of Lorentz Sequence Space

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• 作者：Sung Guen Kim
• 关键词：Mathematics Subject ClassificationPrimary 46A22
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：13
• 期：5
• 页码：2827-2839
• 全文大小：543 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

We classify the exposed polynomials of the unit ball of the space of 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space. In fact, we prove that$$\left.\begin{array}{ll}{\rm exp}B_{{\mathcal P}(^2d_{*}(1, w)^2)} = {\rm ext}B_{{\mathcal{P}}(^2d_{*}(1,w)^2)}{\!\Big\backslash\!} \left\{\pm\left[\frac{x^2-y^2\pm 2{w}xy}{1+{w}^2}\right],\right.\\ \qquad \qquad \quad \quad \pm \left.\left[\frac{1-w}{(1+w)(1+w^2)}(x^2-y^2)\pm\frac{2}{(1+w)^2}xy\right]\right\}.\end{array}\right.$$Mathematics Subject ClassificationPrimary 46A22This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2057788).