次可分解算子的不变子空间格的丰富性

Richness of the Lattice of Invariant Subspaces for Subdecomposable Operators

证明了一类次可分解算子的不变子空间格是丰富的,并举例说明存在Hilbert空间上的有界线性算子T,它有无穷多个不变子空间,但是它的不变子空间格Lat(T)不丰富．

In this paper, we show that the lattice of invariant subspaces for a class of subdecomposable operators is rich. Moreover, we provide a counter-examples on a Hilbert space in which the operator T has infinitely many invariant subspaces while the invariant subspace lattice Lat（T） for T is not rich.