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Operators with expansive m-isometric liftings

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Abstract

We investigate the bounded linear operators T on a Hilbert space \(\mathcal {H}\) which have expansive m-isometric liftings for some integer \(m\ge 2\). We refer to such liftings which are analytic, and we characterize the minimal liftings S under the condition \(S^*S\mathcal {H}\subset \mathcal {H}\). We also describe the operators which have liftings satisfying this condition and are induced by intertwining relations with compressions of m-isometries, or by complete polynomial domination with m-isometries.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, “Lucian Blaga” University of Sibiu, Sibiu, Romania

    Laurian Suciu

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  1. Laurian Suciu
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Communicated by Adrian Constantin.

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We would like to thank the referee for a careful reading of the manuscript and for useful suggestions. The author was supported by a project financed by Lucian Blaga University of Sibiu and Hasso Plattner Foundation research grants LBUS-IRG-2021-07.

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Suciu, L. Operators with expansive m-isometric liftings. Monatsh Math 198, 165–187 (2022). https://doi.org/10.1007/s00605-021-01648-z

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