Annals of Functional Analysis

On operators with closed numerical ranges

Youqing Ji and Bin Liang

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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 ε>0, then there exists a compact operator K with norm less than ε 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

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

Received: 14 May 2017
Accepted: 28 May 2017
First available in Project Euclid: 6 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A12: Numerical range, numerical radius
Secondary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47B20: Subnormal operators, hyponormal operators, etc.

numerical range compact perturbation weighted shifts hyponormal operators


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.

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