Aron–Berner extensions of triple maps with application to the bidual of Jordan Banach triple systems
Aron–Berner extensions of triple maps with application to the bidual of Jordan Banach triple systems
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三重映射的 Aron-Berner 扩展及其应用于 Jordan Banach 三重系统的双向
DOI：
10.1016/j.laa.2019.07.009
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发表时间：
2019
影响因子：
1.1
通讯作者：
A. M. Peralta
中科院分区：
文献类型：
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作者：
AminAllah Khosravi;H. R. E. Vishki;A. M. Peralta
通过推广双线性映射的Arens正则性的概念，我们说Banach空间的Cartesian积上的有界三线性映射是Aron-Berner正则的，当它对双对偶空间的Cartesian积的六个Aron-Berner扩张都重合时.本文给出了某些三线性映射的Aron-Berner正则性的一些结果。然后，我们专注于一个Jordan Banach三元系（E，π）的双对偶，E，并研究在这些条件下，E本身是一个Jordan Banach三元系下的每一个阿龙-Berner扩张的三重积π。我们还比较了这六个三重产品所产生的某些超滤的基础上的超幂制定的原则，当地的自反性。特别是，我们研究了Aron-Berner三重产品的双对偶的JB的一个三重的关系，所谓的Dineen定理。其中包括一些有启发性的例子，也有一些问题有待解决。
By extending the notion of Arens regularity of bilinear mappings, we say that a bounded trilinear map on the Cartesian product of Banach spaces is Aron–Berner regular when all its six Aron–Berner extensions to the Cartesian product of the bidual spaces coincide. We give some results on the Aron–Berner regularity of certain trilinear maps. We then focus on the bidual, E⁎⁎, of a Jordan Banach triple system (E, π), and investigate those conditions under which E⁎⁎ is itself a Jordan Banach triple system under each of the Aron–Berner extensions of the triple product π. We also compare these six triple products with those arising from certain ultrafilters based on the ultrapower formulation of the principle of local reflexivity. In particular, we examine the Aron–Berner triple products on the bidual of a JB⁎-triple in relation with the so-called Dineen's theorem. Some illuminating examples are included and some questions are also left undecided.
Banach空间的一些几何常数——统一方法
DOI：
--
发表时间：
2008
期刊：
Banach and Function spaces II
影响因子：
--
作者：
Yasuji;Takahashi
通讯作者：
Takahashi