Hilbert space operators with two-isometric dilations Article Swipe

View

Related Concepts

Mathematics Hilbert space Isometry (Riemannian geometry) Pure mathematics Quasinormal operator Operator (biology) Operator theory Compact operator on Hilbert space Space (punctuation) Multiplication operator Mathematical analysis Compact operator Finite-rank operator Banach space Computer science Biochemistry Chemistry Gene Extension (predicate logic) Operating system Repressor Programming language Transcription factor

Cătălin Badea , Laurian Suciu , Laurian Suciu , Department of Mathematics and Informatics, ``Lucian Blaga'' University of Sibiu, Roumania ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.7900/jot.2020feb05.2298 · OA: W2919720579

A continuous linear Hilbert space operator S is said to be a 2-isometry if the operator S and its adjoint S∗ satisfy the relation S∗2S2−2S∗S+I=0. We study operators having liftings or dilations to 2-isometries. The adjoint of an operator which admits such liftings is the restriction of a backward shift on a Hilbert space of vector-valued analytic functions. These results are applied to concave operators and to operators similar to contractions. Two types of liftings to 2-isometries, as well as the extensions induced by them, are constructed and isomorphic minimal liftings are discussed.