High order isometric liftings and dilations

0541264 - MÚ 2022 RIV PL eng J - Článek v odborném periodiku
Badea, C. - Müller, Vladimír - Suciu, L.
High order isometric liftings and dilations.
Studia mathematica. Roč. 258, č. 1 (2021), s. 87-101. ISSN 0039-3223. E-ISSN 1730-6337
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: m-isometric lifting * m-isometric dilation * convex operator * Foguel-Hankel operator
Obor OECD: Pure mathematics
Impakt faktor: 0.914, rok: 2021
Způsob publikování: Omezený přístup
http://dx.doi.org/10.4064/sm200330-25-8

We show that a Hilbert space bounded linear operator has an m-isometric lifting for some integer m≥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.
Trvalý link: http://hdl.handle.net/11104/0318854