On the numerical index of polyhedral Banach spaces

被引：22
|
作者：
Sain, Debmalya [1 ]
Paul, Kallol [2 ]
Bhunia, Pintu [2 ]
Bag, Santanu [3 ]
机构：
[1] Indian Inst Sci, Dept Math, Bengaluru 560012, Karnataka, India
[2] Jadavpur Univ, Dept Math, Kolkata 700032, India
[3] Vivekananda Coll Women, Dept Math, Kolkata 700008, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 577卷
关键词：
Polyhedral Banach spaces; Numerical radius; Numerical index; Face of a polyhedron;
D O I：
10.1016/j.laa.2019.04.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite dimensional real polyhedral Banach space, by considering the action of only finitely many functionals, on the unit sphere of the space. We further obtain the exact numerical index of a family of 3-dimensional polyhedral Banach spaces for the first time, in order to illustrate the applicability of our method. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：121 / 133
页数：13
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