  Recently J.A.Anquela, T.Cort\'es, and H.Petersson proved that for elements
$x, y$ in a non-degenerate Jordan algebra $J$, the relation $x \circ y = 0$
implies that the $U$-operators of $x$ and $y$ commute: $U_xU_y = U_yU_x$. We
show that the result may be not true without the assumption on non-degeneracity
of $J$. We give also a more simple proof of the mentioned result in the case of
linear Jordan algebras, that is, when $char\, F\neq 2$.
