On invariant subspaces of subdecomposable operators

Abstract

In this paper, we prove the Mohebi-Radjabalipour Conjecture under an additional condition, and obtain a new invariant subspace theorem for subdecomposable operators. Our main results contain known results in the literature as special cases. Moreover, we give some specific examples to illustrate that the conditions in our theorem are significantly weaker, simpler and more nature than those in the known results.