On the class of Banach spaces with James constant |
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| Authors: | Naoto Komuro Kichi‐Suke Saito Ryotaro Tanaka |
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| Affiliation: | 1. Department of Mathematics, Hokkaido University of Education, Asahikawa campus, Asahikawa, Japan;2. Department of Mathematics, Faculty of Science, Niigata University, Niigata, Japan;3. Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan |
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| Abstract: | In this paper, we study the class of Banach spaces with James constant  . It is shown that, for a Banach space of three or more dimensions, the James constant becomes  if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on  with James constant  are completely characterized in terms of convex functions on the unit interval, which provides many new examples of such norms other than the Euclidean or regular octagonal norms. However, it is also shown that there exist two‐dimensional normed spaces with James constant  outside of the family of symmetric absolute norms. |
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| Keywords: | James constant inner product space absolute norm symmetric norm 46B20 |
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