Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (912 KB) | Metadata | Table of Contents | ZAA summary
Published online: 1998-06-30
On the Geometric Structure of Minimal Dilations on Hilbert $C*$-ModulesD. Popovici (1) West University of Timisoara, Romania
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.
Keywords: Hilbert $C*$-modules, adjointable contractions, Wold-type decompositions, isometric and unitary dilations
Popovici D.: On the Geometric Structure of Minimal Dilations on Hilbert $C*$-Modules. Z. Anal. Anwend. 17 (1998), 379-392. doi: 10.4171/ZAA/828