【摘要】 对于与Volterra算子V交换的算子T,通过构造和计算,证明了:如果f(x)=1是T的一个循环向量,则A′(V)=A′(T).因而V的不变子空间都是T的超不变子空间.此外还证明了T是单的当且仅当T是稠值域的,进而σ(T)=σe(T)=σlre(T).更多还原

【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）.更多还原