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

Authors

  • Zbigniew Burdak University of Agriculture Krakow, Department of Applied Mathematics
  • Wiesław Grygierzec University of Agriculture Krakow

Abstract

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.

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Published

2020-04-01

How to Cite

Burdak, Z., & Grygierzec, W. (2020). On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 19, 121–139. Retrieved from https://studmath.uken.krakow.pl/article/view/7928

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