Abstract
ABSTRACT Let denote the class of operators A acting on a complex Hilbert space such that where and are the maximal numericl range, the spectrum of A, respectively, and co stands for the convex hull. In this paper, we show that the class contains hyponormal operators. We also show that if two operators and have the same closure of the numerical range or have the same spectrum, then they also have the same maximal numerical range. An affirmative answer to the question 2.16 in Fialkow [Elementary operators and applications. Proceedings of the International Workshop; Bleuberen; 1991. p. 55–113] is also given.
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