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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 2, 1998, pp. 379–392
DOI: 10.4171/ZAA/828

Published online: 1998-06-30

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

D. Popovici[1]

(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