English

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 mm-isometric lifting for some integer m1m\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 mm-isometric dilation. We also study 22-isometric liftings of convex operators and 33-isometric liftings of Foguel-Hankel operators.

Keywords

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

R2 v1 2026-06-23T14:30:06.457Z