<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The <italic>n</italic>-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 <italic>n</italic>-tuple. A series of such liftings leads to an isometric dilation of the <italic>n</italic>-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 <italic>n</italic>-tuple has an isometric dilation.</p></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.

On dilation and commuting liftings of <italic>n</italic>-tuples of commuting Hilbert space contractions

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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

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...

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

Published Online: Dec 31, 2020

Page range: 121 - 139

Received: Jan 22, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0010

Keywords
dilation, lifting, von Neumann inequality

© 2020 Zbigniew Burdak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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

Published Online: Dec 31, 2020

Page range: 121 - 139

Received: Jan 22, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0010

Keywordsdilation, lifting, von Neumann inequality

© 2020 Zbigniew Burdak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
dilation, lifting, von Neumann inequality