Abstract
A bounded linear operator A acting on a separable complex Hilbert space H is called C-normal with respect to some conjugation C on H if $$CA^*AC=AA^*$$ . In the present paper, we show that every bounded linear operator A on H can be perturbed by finite-rank operator F with norm as small as desired so that $$A+F$$ is not C-normal with respect to any conjugation C.
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