When does the equality J(X^*) = J(X) holds?
When does the equality J(X^*) = J(X) holds?
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等式 J(X^*) = J(X) 什么时候成立？
DOI：
10.1007/s10114-015-4539-3
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Ryotaro Tanaka
中科院分区：
文献类型：
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作者：
Kichi-Suke Saito;Masahiro Sato;Ryotaro Tanaka
在本文中，我们考虑了关于James常数的下列问题：对于Banach空间X，等式J(X*)=J(X)何时成立？一般情况下，Banach空间的James常数与其对偶空间的James常数并不重合。事实上，我们已经有了二维赋范空间的反例，它们要么配备对称范数，要么配备绝对范数。然而，如果二维空间X上的范数既是对称的又是绝对的，则等式J(X*)=J(X)成立。这为二维情况下的问题提供了一个全局答案。
In this paper, we consider the following problem about the James constant: When does the equalityJ(X*) =J(X) hold for a Banach spaceX? It is known that the James constant of a Banach space does not coincide with that of its dual space in general. In fact, we already have counterexamples of two-dimensional normed spaces that are equipped with either symmetric or absolute norms. However, we show that if the norm on a two-dimensional spaceXis both symmetric and absolute, then the equalityJ(X*) =J(X) holds. This provides a global answer to the problem in the two-dimensional case.