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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-5,
author = {Santanu Dey},
title = {Standard commuting dilations and liftings},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {87-94},
zbl = {1272.47012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-5}
}
Santanu Dey. Standard commuting dilations and liftings. Colloquium Mathematicae, Tome 126 (2012) pp. 87-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-5/