| Co-Investigator(Kenkyū-buntansha) |
WATANABE Keiichi Faculty of Science, Niigata University, Associate Professor, 理学部, 助教授 (50210894)
TAKAHASHI Yasuji Okayama Prefectural University, Faculty of Computer Science and System Engineering, Professor, 情報工学部, 教授 (30001853)
KATO Mikio Kyushu Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (50090551)
SUZUKI Tomonari Graduate School of Science and Technology, Niigata University, Assistant, 大学院・自然科学研究科, 助手 (00303173)
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| Research Abstract |
The study of the Banach space theory is an important and useful object in the every branch of Mathematics and has the many application. In this research, we study, the von Neumann-Jordan constant of Banach spaces, in particular, finite dimensional Banach spaces. At first, for 2-dimensional Banach space, we show that there is a one-to-one correspondence between the set of all normalized absolute norms and the set of special class of convex functions on [0,1]. We calculate or estimate the von Neumann-Jordan constant of 2-dimensional Banach spaces using the convex function. Further, we study the geometrical structure of Banach spaces using the corresponding convex functions. Moreover, we extend these results to the finite dimensional Banach spaces. We continue to extend them to the infinite Banach spaces, in particular, sequence spaces with absolute norm.
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