real analysis – sandwich theorem

Does sandwich theorem hold for divergent sequences?
Given a divergent sequence ${v_n},$ can we find 2 sequences ${u_n}$ and ${w_n},$ such that $${u_n} < {v_n} < {w_n},$$ and if $u_n}$ and ${w_n}$ diverges to $L,$ then can we conclude ${v_n}$ also diverges to $L?$