Brown-Halmos type theorems of Toeplitz+Hankel operators (Q6044193)

For \(f\in L^{\infty}\), let \(T_{f}\) and \(H_{f}\) be Toeplitz and Hankel operators on Hardy space respectively. The main purpose of the present paper is to discuss Brown-Halmous type theorems of Toeplitz+Hankel operators on Hardy space. Firstly, the author provides a criterion for \((T_{u}+H_{v})(T_{f}+H_{f})\) to be a Toeplitz+Hankel operators. Then a complete characterization of the commutativity of Toeplitz+Hankel operators is given.