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In the paper we give a characterization of a $w^*$-continuous orthogonalvector field $F$ over an $W^*$-algebra $\mathcal{N}$ of type $I_2$ in terms ofreductions $F$ on the center of $\mathcal{N}$. As an application it is obtaineda proof of the assertion that an arbitrary $w^*$-continuous orthogonal vectorfield over a $W^*$-algebra of type $I_2$ is stationary.

A characterization of orthogonal vector fields over ${\bf W^*}$-algebras of type ${\bf I_2}$