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.
"On operators with closed numerical ranges." Ann. Funct. Anal. 9 (2) 233 - 245, May 2018. https://doi.org/10.1215/20088752-2017-0051