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,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/3