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

Michał Buchała

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

Functional Analysis 2025-07-11 v1

Authors: Michał Buchała

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.

Keywords

operator theory on hilbert spaces operator theory

Cite

@article{arxiv.2507.07252,
  title  = {Every expansive $ m $-concave operator has $ m $-isometric dilation},
  author = {Michał Buchała},
  journal= {arXiv preprint arXiv:2507.07252},
  year   = {2025}
}

Comments

11 pages

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