On the geometric structure of minimal dilations on Hilbert \(C^*\)-modules
Summary: 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. Foiaş 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 admit a Wold-type decomposition, a condition which also assures the complementability of the residual part space of the minimal unitary dilation.
scientific article; zbMATH DE number 1182354