Displaying similar documents to “Perturbations of operators similar to contractions and the commutator equation”

Standard commuting dilations and liftings

Santanu Dey (2012)

Colloquium Mathematicae

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We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.

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

Zbigniew Burdak, Wiesław Grygierzec (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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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.