Tensor product of nn-isometries

A Hilbert space operator A is an m-isometry if∑k=0m(-1)kmkA∗m-kAm-k=0.We prove that the tensor product of an m-isometry A with an n-isometry B   is an m+n-1m+n-1 isometry. This proves a conjecture of Botelho and Jamison [5, Remark 5.1].