On Decomposition for Pairs of Twisted Contractions

This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in \(C_{00}\) $C_{00}$ . The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair \((T,V^*)\) $(T,V^{\ast })$ of twisted operators with T as a contraction and V as an isometry, there exists a unique (up to unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of T. Finally, we have given a characterization for pairs of doubly twisted isometries.