AOP mappings and the distance to the scalar multiples of isometries

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Zhang, Ye¹  Chen, Yanni²  Hadwin, Don²  Kong, Liang³ 

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

[2] Univ New Hampshire, Dept Math, Durham, NH 03824 USA

[3] Shangluo Univ, Inst Appl Math, Shangluo 726000, Peoples R China

关键词: Approximate orthogonality;    Orthogonality preserving mappings;    Linear operators;    Minimum modulus;    Isometries;   

DOI  :  10.1016/j.jmaa.2015.05.031

来源: Elsevier

【 摘 要 】

In this paper, linear epsilon-orthogonality preserving mappings are studied. We define (epsilon) over cap (T) as the smallest epsilon for which T is epsilon-orthogonality preserving, and then derive an exact formula for (epsilon) over cap (T) in terms of parallel to Th parallel to and the minimum modulus m (T) of T. We see that epsilon-orthogonality preserving mappings (for some epsilon < 1) are exactly the operators that are bounded from below. We improve an upper bound in the stability equation given in [7, Theorem 2.3], which was thought to be sharp. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free