Numerical ranges and complex symmetric operators in semi-inner-product spaces

被引：0

作者：

An, Il Ju ^{[1
]}

Heo, Jaeseong ^{[2
]}

机构：

[1] Kyung Hee Univ, Dept Appl Math, Yongin 17104, Gyeonggi Do, South Korea

[2] Hanyang Univ, Res Inst Nat Sci, Dept Math, Seoul 04763, South Korea

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2022年 / 2022卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Semi-inner-product space; Numerical range; Conjugations; Complex symmetric operators; Generalized adjoint;

D O I：

10.1186/s13660-022-02886-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the numerical range of a bounded linear operator on a semi-inner-product space. We compute the numerical ranges of some operators on l(2)(p)(C) (1 <= p < infinity) and show that the numerical range of the backward shift on an infinite-dimensional space l(p) is the open unit disc. We define a conjugation and a complex symmetric operator on a semi-inner-product space and discuss complex symmetry in the dual space. We prove some properties of a generalized adjoint of a complex symmetric operator. We also show that the numerical range of the complex conjugation on l(n)(p) (n >= 2) is the closed unit disc. Finally, we discuss the sequentially essential numerical ranges of operators on a semi-inner-product space.

引用

页数：15