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On the class of Banach spaces with James constant 2
Author(s) -
Komuro Naoto,
Saito KichiSuke,
Tanaka Ryotaro
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500238
Subject(s) - mathematics , banach space , constant (computer programming) , norm (philosophy) , pure mathematics , class (philosophy) , regular polygon , lp space , unit sphere , normed vector space , euclidean space , mathematical analysis , geometry , computer science , programming language , artificial intelligence , political science , law
In this paper, we study the class of Banach spaces with James constant 2 . It is shown that, for a Banach space of three or more dimensions, the James constant becomes 2 if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on R 2 with James constant 2 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 2 outside of the family of symmetric absolute norms.