## Annals of Functional Analysis

### On operators with closed numerical ranges

#### Abstract

In this article we investigate the numerical ranges of several classes of operators. It is shown that, if we let $T$ be a hyponormal operator and let $\varepsilon\gt 0$, then there exists a compact operator $K$ with norm less than $\varepsilon$ such that $T+K$ is hyponormal and has a closed numerical range. Moreover we prove that the statement of the above type holds for other operator classes, including weighted shifts, normaloid operators, triangular operators, and block-diagonal operators.

#### Article information

Source
Ann. Funct. Anal., Volume 9, Number 2 (2018), 233-245.

Dates
Accepted: 28 May 2017
First available in Project Euclid: 6 December 2017

https://projecteuclid.org/euclid.afa/1512529266

Digital Object Identifier
doi:10.1215/20088752-2017-0051

Mathematical Reviews number (MathSciNet)
MR3795088

Zentralblatt MATH identifier
06873700

#### Citation

Ji, Youqing; Liang, Bin. On operators with closed numerical ranges. Ann. Funct. Anal. 9 (2018), no. 2, 233--245. doi:10.1215/20088752-2017-0051. https://projecteuclid.org/euclid.afa/1512529266

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