Complex symmetric operators and isotropic vectors on Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Cho, Muneo¹  Hur, Injo²  Lee, Ji Eun³ 

[1] Kanagawa Univ, Dept Math, Hiratsuka, Kanagawa 2591293, Japan

[2] Chonnam Natl Univ, Dept Math Educ, 77 Yongbong Ro, Gwangju 61186, South Korea

[3] Sejong Univ, Dept Math & Stat, Seoul 05006, South Korea

关键词: Banach space;    Complex symmetric operator;    Conjugation;    Isotropic;   

DOI  :  10.1016/j.jmaa.2019.06.049

来源: Elsevier

【 摘 要 】

In this paper, we generalize the concepts of isotropic vectors and complex symmetric operators from Hilbert spaces to Banach spaces via their dual spaces. With this extension we show the existence of isotropic vectors on Banach spaces whose dimension is at least two and the relation between the simplicity of an eigenvalue and the non-existence of its isotropic eigenvectors. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free