Operators with closed numerical ranges in nest algebras
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- by Youqing Ji and Bin Liang PDF
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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 $\|K\|<\varepsilon$ 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.
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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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2563-2575
- MSC (2010): Primary 47L35, 47A12; Secondary 47A55
- DOI: https://doi.org/10.1090/proc/13948
- MathSciNet review: 3778158