The transformations referred to in the title of the paper under review are certain specific measure-preserving transformations \(T_d:({\mathbb T}^\infty)^d\to ({\mathbb T}^\infty)^d\) with \(d\geq 2\), which then define the unitary operators \(W_d: {\mathcal H}_d\to{\mathcal H}_d\), \(\phi\mapsto\phi\circ T_d\), where \({\mathcal H}_d=L^2(({\mathbb T}^\infty)^d)\). The main results provide sufficient conditions on \(T_d\) in order that the operator \(W_d\) be strongly mixing in \({\mathcal H}_d\ominus{\mathcal H}_1\) and \(T_d\) be uniquely ergodic. Additional conditions ensure that \(W_d\) has countable Lebesgue spectrum in \({\mathcal H}_d\ominus{\mathcal H}_1\).