Mingxue Liu

Abstract
In 1978, S. Brown proved that each subnormal operator has an invariant subspace.In 1981, C. Apostol obtained an invariant subspace theorem on unconditionally decomposable operators. In this paper, we prove the Mohebi-Radjabalipour Conjecture under an additional condition, and obtain an invariant subspace theorem on subdecomposable operators. Our theorem contains the results of S. Brown and C. Apostol as special cases.