On $C_{0·}$ multi-contractions having a regular dilation
Commuting multi-contractions of class C0· and having a regular isometric dilation are studied. We prove that a polydisc contraction of class C0· is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.