Abstract
A bounded linear operator A acting on a complex Hilbert space H is called complex symmetric if there exists a conjugation C on H such that CAC=A⁎. In this paper, we prove that a large class of rank-one perturbations of normal operators are complex symmetric. We show also that every operator A can be approximated by non-complex symmetric operators of the form A+F where F is a finite rank operator whose range can be controlled.
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