Some algebraic properties of Toeplitz and Hankel operators on polydisk (Q1401629)

Let \(D^n(T^n)\), \(n\geq1\), be the polydisk (\(n\)-torus) and \(P\) be the projection from \(L^2(T^n)\) onto the Hardy space \(H^2(D^n)\). The author considers some properties of the Toeplitz operator \(T_fh=P(fh)\) and the (big) Hankel operator \(H_fh=(I-P)(fh)\) with symbol \(f\in{L^\infty}(T^n)\). Let \(\widehat{H_f}\) denote the small Hankel operator \(\widehat{H_f}h=P(f(z)h(\overline{z}))\), \(z\in{D^n}\). The author characterizes when the product of two Toeplitz operators (or two small Hankel operators) is also a Toeplitz (respectively, a Hankel) operator.