The Banach-Mazur distance between the trace classes $c\sp{n}\sb{p}$

The Banach-Mazur distance between $l_2^n\hat \otimes l_2^m$ and $l_2^n\hat \hat \otimes l_2^m$ is shown to be of the order $\sqrt {\min (n,m)}$. Our proof yields that the distance between the trace classes $c_p^n$ and $c_q^n$ is of the same order as $d(l_p^n,l_q^n)$.