算子的超不变子空间与Wolf谱

Hyperinvariant Subspaces and Wolf Spectrum of Operators

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).

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).