A COMPLETE CHARACTERIZATION OF BIRKHOFF-JAMES ORTHOGONALITY IN INFINITE DIMENSIONAL NORMED SPACE

被引：26
|
作者：
Sain, Debmalya [1 ]
Paul, Kallol [2 ]
Mal, Arpita [2 ]
机构：
[1] Indian Inst Sci, Dept Math, Bengaluru 560012, India
[2] Jadavpur Univ, Dept Math, Kolkata 700032, India
来源：
JOURNAL OF OPERATOR THEORY | 2018年 / 80卷 / 02期
关键词：
Orthogonality; linear operators; norm attainment; smoothness; SMOOTH POINTS; OPERATORS; MAPPINGS;
D O I：
10.7900/jot.2017oct20.2190
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an application of the results obtained, we prove a simple but useful characterization of Birkhoff-James orthogonality of bounded linear functionals defined on a real normed linear space, provided the dual space is strictly convex. We also provide separate necessary and sufficient conditions for smoothness of bounded linear operators on infinite dimensional normed linear spaces.
引用
收藏
页码：399 / 413
页数：15
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