Singular unitary dilations

We study the problem of determining which bounded linear operator on a Hilb ert space can be dilated to a singular unitary operator. Same of the partia l results we obtained are (1) every strict contraction has a diagonal unita ry dilation, (2) every C-0 contraction has a singular unitary dilation, and (3) a contraction with one of its defect indices finite has a singular uni tary dilation if and only if it is the direct sum of a singular unitary ope rator and a C-0(N) contraction. Such results display a scenario which is in marked contrast to that of the classical case where we have the absolute c ontinuity of the minimal unitary power dilation of any completely nonunitar y contraction.