On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions

Zbigniew Burdak, Wiesław Grygierzec


The n-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 n-tuple. A series of such liftings leads to an isometric dilation of the n-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 n-tuple has an isometric dilation.


dilation; lifting; von Neumann inequality

Mathematics Subject Classification (2010)

Primary 47A20; Secondary 47A50


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