On $C_{0·}$ multi-contractions having a regular dilation

Dan Popovici

C_{0 \cdot}

multi-contractions having a regular dilation

Dan Popovici

Studia Mathematica, Tome 166 (2005), p. 297-302 / Harvested from The Polish Digital Mathematics Library

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Résumé

Commuting multi-contractions of class $C_{0 \cdot}$ and having a regular isometric dilation are studied. We prove that a polydisc contraction of class $C_{0 \cdot}$ is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.

Publié le : 2005-01-01

Zbl 1088.47005

EUDML-ID : urn:eudml:doc:285291

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Dan Popovici. On $C_{0·}$ multi-contractions having a regular dilation. Studia Mathematica, Tome 166 (2005) pp. 297-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-6/