On the ascent of composition operators (Q1803515)

A misstatement in a paper by \textit{R. K. Singh} and \textit{R. David Chandrakumar} [Indian J. Pure Appl. Math. 14, 1233-1237 (1983; Zbl 0543.47022)] is pointed out and corrected. Furthermore, two theorems about composition operators on \(L^ 2(X,\mu)\) are stated and proved. The only curiosity about the theorems is that they remain true for general bounded linear operators on a Hilbert space. The proofs are elementary, and the theorems are illustrated with examples.