High order isometric liftings and dilations
Functional Analysis
2020-08-25 v3 Spectral Theory
Abstract
We show that a Hilbert space bounded linear operator has an -isometric lifting for some integer 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 -isometric dilation. We also study -isometric liftings of convex operators and -isometric liftings of Foguel-Hankel operators.
Cite
@article{arxiv.2003.12741,
title = {High order isometric liftings and dilations},
author = {Catalin Badea and Vladimir Müller and Laurian Suciu},
journal= {arXiv preprint arXiv:2003.12741},
year = {2020}
}
Comments
15 pages. Paper (dedicated to Ciprian Foias) to appear in Studia Math