On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions-Reference-Cited by-同舟云学术

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

Published:2020-12-01 Issue:1 Volume:19 Page:121-139
ISSN:2300-133X
Container-title:Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
language:en
Short-container-title:

Author:

Burdak Zbigniew¹,Grygierzec Wiesław²

Affiliation:

1. University of Agriculture Krakow , Department of Applied Mathematics , Balicka 253C, Kraków, 30-198 , Poland

2. University of Agriculture Krakow , al. Mickiewicza 21, Kraków, 31-120 , Poland

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/aupcsm-2020-0010

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