Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane

We study effectively hyperbolic operators $P$ with triple characteristics points lying on $t= 0$. Under some conditions on the principal symbol of $P$ one proves that the Cauchy problem for $P$ in $[0, T] \times U$ is well posed for every choice of lower order terms. Our results improves those in [11] since we don't assume the condition (E) of [11] satisfied.