Abstract: Let T be in the commutant of Volterr a operator V, by construction and calculation, it is proved that if the function f(x)=1 is a cyclic vector of T, then A′(V)=A′(T).Thus all the invariant subspaces of V are hyperinvariant for T. Moreover, it is also proved that if only if ker T=｛0｝ran T=H, σ(T)=σ_e(T)=σ_lre(T).

Key words: Volterra operator, commutant, cyclic vector, hyperinvariant subspace, unitarily self-adjiont, range-dense, Wolf spactrum