ON SYMMETRY OF BIRKHOFF-JAMES ORTHOGONALITY OF LINEAR OPERATORS ON FINITE-DIMENSIONAL REAL BANACH SPACES

被引：19

作者：

Sain, Debmalya ^{[1
]}

Ghosh, Puja ^{[1
]}

Paul, Kallol ^{[1
]}

机构：

[1] Jadavpur Univ, Dept Math, Kolkata 700032, W Bengal, India

来源：

OPERATORS AND MATRICES | 2017年 / 11卷 / 04期

关键词：

Birkhoff-James orthogonality; symmetry of orthogonality; bounded linear operators; finite dimensional Banach spaces; NORM ATTAINMENT;

D O I：

10.7153/oam-2017-11-75

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize left symmetric linear operators on a finite dimensional strictly convex and smooth real normed linear space X, which answers a question raised recently by one of the authors in [7] [D. Sain, Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces, J. Math. Anal. Appl. 447 (2017) 860-866]. We prove that T is an element of B(X) is left symmetric if and only if T is the zero operator. If X is two-dimensional then the same characterization can be obtained without the smoothness assumption. We also explore the properties of right symmetric linear operators defined on a finite dimensional real Banach space. In particular, we prove that smooth linear operators on a finite-dimensional strictly convex and smooth real Banach space can not be right symmetric.

引用

页码：1087 / 1095

页数：9