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

Zbigniew Burdak; Wiesław Grygierzec

doi:10.2478/aupcsm-2020-0010

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

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 19 (2020): Issue 1 (December 2020)

By: Zbigniew Burdak and Wiesław Grygierzec

Open Access

|Dec 2020

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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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2020-0010 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 121 - 139

Submitted on: Jan 22, 2020

Published on: Dec 31, 2020

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

dilation,

lifting,

von Neumann inequality

Related subjects:

Mathematics,

General mathematics

© 2020 Zbigniew Burdak, Wiesław Grygierzec, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 19 (2020): Issue 1 (December 2020)