Description of orthogonal vector fields over $W^*$-algebra of type $I_2$

In the paper we give a characterization of a $w^*$-continuous orthogonal vector field $F$ over a $W^*$-algebra of type $I_2$ in terms of reductions of $F$ on the center of the algebra. As an application we obtain a new proof of the assertion that an arbitrary $w^*$-continuous orthogonal vector field over a $W^*$-algebra of type $I_2$ is stationary.