@article{Burdak_Grygierzec_2020, title={On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions}, volume={19}, url={https://studmath.up.krakow.pl/article/view/7928}, abstractNote={<p>The <em>n</em>-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an <em>n</em>-tuple. A series of such liftings leads to an isometric dilation of the <em>n</em>-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite <em>n</em>-tuple has an isometric dilation.</p>}, journal={Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica}, author={Burdak, Zbigniew and Grygierzec, Wiesław}, year={2020}, month={Apr.}, pages={121–139} }