On the geometric structure of minimal dilations on Hilbert \(C^*\)-modules
type: Item
instance of: scholarly article
title: On the geometric structure of minimal dilations on Hilbert \(C^*\)-modules
zbMATH Open document ID: 0914.47006
DOI: 10.4171/ZAA/828
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-06-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1182354
zbMATH Keywords: unitary extension
zbMATH Keywords: isometry on a Hilbert \(C^*\)-module
zbMATH Keywords: adjointable contraction
zbMATH Keywords: Wold-type decomposition
author: Dan Popovici
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1182354