Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Operators with closed numerical ranges in nest algebras


Authors: Youqing Ji and Bin Liang
Journal: Proc. Amer. Math. Soc. 146 (2018), 2563-2575
MSC (2010): Primary 47L35, 47A12; Secondary 47A55
DOI: https://doi.org/10.1090/proc/13948
Published electronically: March 12, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper, we continue our research on numerical ranges of operators. With newly developed techniques, we show that

Let $ \mathcal {N}$ be a nest on a Hilbert space $ \mathcal {H}$ and $ T\in \mathcal {T} (\mathcal {N})$, where $ \mathcal {T} (\mathcal {N})$ denotes the nest algebra associated with $ \mathcal {N}$. Then for given $ \varepsilon >0$, there exists a compact operator $ K$ with $ \Vert K\Vert<\varepsilon $ such that $ T+K \in \mathcal {T} (\mathcal {N})$ and the numerical range of $ T+K$ is closed.

As applications, we show that the statement of the above type holds for the class of Cowen-Douglas operators, the class of nilpotent operators and the class of quasinilpotent operators.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47L35, 47A12, 47A55

Retrieve articles in all journals with MSC (2010): 47L35, 47A12, 47A55


Additional Information

Youqing Ji
Affiliation: Department of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email: jiyq@jlu.edu.cn

Bin Liang
Affiliation: Department of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email: liangbinmath@163.com

DOI: https://doi.org/10.1090/proc/13948
Keywords: Nest algebra, numerical range, Cowen-Douglas operator, quasinilpotent operator.
Received by editor(s): August 26, 2017
Received by editor(s) in revised form: September 2, 2017
Published electronically: March 12, 2018
Additional Notes: The first author was supported by National Natural Science Foundation of China (no. 11271150, no. 11531003).
The second author was supported by National Natural Science Foundation of China (no. 11671167).
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society