TY - JOUR
AU - Burdak, Zbigniew
AU - Grygierzec, WiesÅ‚aw
PY - 2020/04/01
Y2 - 2024/09/11
TI - On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 19
IS -
SE - Published
DO -
UR - https://studmath.uken.krakow.pl/article/view/7928
SP - 121-139
AB - <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>
ER -