Lifting intertwining relations (Q1100414)

This note is devoted to the lifting problem for the intertwining relation \(XT^*_ 1=T_ 2X\), where the \(T_ j\), \(j=1,2\), are given contractions and X is a bounded operator. The lifting is possible if and only if X satisfies a stronger condition of boundedness introduced by the authors in the previous paper [Operators of Toeplitz and Hankel type, Acta Sci. Math. (Szeged), in print]. The note includes section which gives a simple proof of the commutant lifting theorem based on completing matrix constructions.