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

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.