Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 2 (2018), 233-245.
On operators with closed numerical ranges
In this article we investigate the numerical ranges of several classes of operators. It is shown that, if we let be a hyponormal operator and let , then there exists a compact operator with norm less than such that 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.
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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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