On $C_{0\cdot }$ multi-contractions having a regular dilation
Volume 170 / 2005
Studia Mathematica 170 (2005), 297-302
MSC: 47A20, 47A13, 47A45.
DOI: 10.4064/sm170-3-6
Abstract
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.
