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arXiv · 2003.12741

High order isometric liftings and dilations

Catalin Badea·Vladimir Müller·Laurian Suciu
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Abstract

We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ 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 $m$-isometric dilation. We also study $2$-isometric liftings of convex operators and $3$-isometric liftings of Foguel-Hankel operators.

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Catalin Badea, Vladimir Müller, Laurian Suciu. 2020-03-28. High order isometric liftings and dilations. https://arxiv.org/abs/2003.12741

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