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 Hubert 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.
Cite this article
D. Popovici, On the Geometric Structure of Minimal Dilations on Hilbert -Modules. Z. Anal. Anwend. 17 (1998), no. 2, pp. 379–392DOI 10.4171/ZAA/828