Standard commuting dilations and liftings
Volume 126 / 2012
Colloquium Mathematicum 126 (2012), 87-94
MSC: Primary 47A20; Secondary 47A13, 47A15, 46L05.
DOI: 10.4064/cm126-1-5
Abstract
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.
