Numerical ranges and complex symmetric operators in semi-inner-product spacesopen access
- Authors
- An, Il Ju; Heo, Jaeseong
- Issue Date
- Nov-2022
- Publisher
- Institute for Ionics
- Keywords
- Semi-inner-product space; Numerical range; Conjugations; Complex symmetric operators; Generalized adjoint
- Citation
- Journal of Inequalities and Applications, v.2022, no.1, pp.1 - 15
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Inequalities and Applications
- Volume
- 2022
- Number
- 1
- Start Page
- 1
- End Page
- 15
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/185202
- DOI
- 10.1186/s13660-022-02886-x
- ISSN
- 1025-5834
- Abstract
- 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 ℓ2p(C)(1 ≤ p< ∞ ) and show that the numerical range of the backward shift on an infinite-dimensional space ℓp 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 ℓnp(n≥ 2 ) is the closed unit disc. Finally, we discuss the sequentially essential numerical ranges of operators on a semi-inner-product space.
- Files in This Item
-
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.