High order isometric liftings and dilations
Volume 258 / 2021
Studia Mathematica 258 (2021), 87-101
MSC: Primary 47A05, 47A20; Secondary 47A15, 47A63.
DOI: 10.4064/sm200330-25-8
Published online: 21 December 2020
Abstract
We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only if the norms of its powers grow polynomially. In analogy with unitary dilations of contractions, we prove that such operators also have an invertible $m$-isometric dilation. We also study $2$-isometric liftings of convex operators and $3$-isometric liftings of Foguel–Hankel type operators.
