Lomonosov's invariant subspace theorem for multivalued linear operators

The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator $T$ on an infinite-dimensional normed space $E$ ``commutes'' with a compact operator $K\neq0,$ i.e., $TK=KT,$ then $T$ has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators. We also provide an application to single-valued linear operators.