Characterization of real inner product spaces by Hermite-Hadamard type orthogonalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Dehghani, Mandi¹  Zamani, Ali² 

[1] Univ Kashan, Fac Math Sci, Dept Pure Math, POB 87317-53153, Kashan, Iran

[2] Farhangian Univ, Dept Math, Tehran, Iran

关键词: Birkhoff-James orthogonality;    Carlsson orthogonality;    Characterization of inner product spaces;    Hermite-Hadamard type orthogonality;    Orthogonality preserving mapping;   

DOI  :  10.1016/j.jmaa.2019.07.002

来源: Elsevier

【 摘 要 】

In this study, we provide some new characterizations of the real inner product spaces using the notion of Hermite-Hadamard (HH) type orthogonalities and by considering their relationships with Birkhoff-James orthogonality. In addition, we investigate the classes of linear mappings that preserve two special types of these orthogonalities. In particular, we show that every HH-I-orthogonality preserving linear mappings is necessarily a scalar multiple of a linear isometry. Finally, we present some other characterizations of real inner product spaces in terms of HH-P-and HH-I-orthogonality preserving mappings. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free