In this paper, we characterize the operators which are unitarily equivalent to truncated Hankel operators. We show that every rank one operator and every $2\times 2$ matrix is unitarily equivalent to a truncated Hankel operator. Furthermore, we get that certain sum of tenser products of truncated Hankel operators is unitarily equivalent to a truncated Hankel operator.
ZHAO, XI and YU, TAO
"Unitary equivalence to truncated Hankel operators,"
Turkish Journal of Mathematics: Vol. 46:
6, Article 22.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/22