An operator on a complex Hilbert space is said to be complex symmetric if can be represented as a symmetric matrix relative to some orthonormal basis for . In this article we explore the stability of complex symmetry under the condition of similarity. It is proved that the similarity orbit of an operator is included in the class of complex symmetric operators if and only if is an algebraic operator of degree at most .
"Similarity orbits of complex symmetric operators." Ann. Funct. Anal. 8 (1) 63 - 74, February 2017. https://doi.org/10.1215/20088752-3750041