We define a truncated composition operator on the spaces P_n of n-degree polynomials with complex coefficients. After doing so, we concern ourselves with the complex symmetry of such operators, that is, whether there is an orthonormal basis that gives them a symmetric matrix representation.
Jansen, Ruth and Rousseau, Rebecca K., "Complex Symmetry of Truncated Composition Operators" (2017). Mathematics Student Scholarship. 1.