On the Geometric Structure of Minimal Dilations on Hilbert C*-Modules

We build a unitary extension for an isometry on a Hilbert C*-module and then, with this extension help, we obtain the minimal unitary dilation for an adjointable contraction starting from one of its isometric dilations. Having as a starting point a result of B.Sz. - Nagy and C. Foias regarding the geometric structure of the minimal unitary dilations for Hilbert space contractions we prove that this structure maintains itself on Hilbert modules. Finally, we present a necessary and sufficient condition on the minimal isometric dilation in order to admits a Wold-type decomposition, condition which also assures the complementability of the residual part space of the minimal unitary dilation.