关键词: 复对称算子, 斜对称算子, Toeplitz算子, 截断Toeplitz算子, 加权移位, 部分等距, 约化子空间

Abstract: A complex symmetric  operator refers to a linear operator with a symmetric matrix representation  on a  Hilbert space. We review the main research  advances  and  several open problems of complex symmetric operators in recent years, involving special complex symmetric operators, reducing subspaces, the norm closure problem, and algebraic properties  and so on.

Key words: complex symmetric operator, skew symmetric operator, Toeplitz operator, truncated Toeplitz operator, weighted shift, partial isometry, reducing subspace