Construction of dilations (Q1191723)

Sz.-Nagy proved the existence for each contraction \(T\) of a unitary dilation \(U\) on a larger Hilbert space, i.e. \((T^ n h,h')=(U^ n h,h')\); \(h,h'\in{\mathcal H}\), \(n\geq 0\). The classical results of Sz.-Nagy are considered in the paper from the algebraic point of view. The interpretation of the Julia operator \[ J(T)=\begin{pmatrix} T &D(T^*)\\ d(T) &-T^*\end{pmatrix} \] is given.