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Liang, Bin
Journal of mathematical analysis and applications, 04/2023, Letnik: 520, Številka: 2Journal Article
A bounded linear operator T:H→H is said to be complex symmetric if there exists a conjugation C on H such that CT⁎C=T. In this paper, we study the numerical ranges of complex symmetric operators. We show that every complex symmetric operator T on H has a small compact perturbation being complex symmetric and having a closed numerical range. We also show that this holds for skew symmetric operators but fails to hold for unitary operators.
