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arXiv · 2507.07252

Every expansive $ m $-concave operator has $ m $-isometric dilation

Michał Buchała
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Abstract

The aim of this paper is to obtain $ m $-isometric dilation of expansive $ m $-concave operator on Hilbert space. The obtained dilation is shown to be minimal. The matrix representation of this dilation is given. It is also proved that in case of 3-concave operators the assumption on expansivity is not necessary. The paper contains an example showing that minimal $ m $-isometric dilations may not be isomorphic.

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Michał Buchała. 2025-07-09. Every expansive $ m $-concave operator has $ m $-isometric dilation. https://arxiv.org/abs/2507.07252

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