Some Resits on Invariant Subspace Problem

<正> In preaent paper we obtain some results concerning transitive algebras, reductive algebras,and reductive operators. In section 1, we give several sufficient conditions which imply the strongdensity of a transitive algebra. One of these, as an improvement of the results in [5], partiallyanswers a question in [2] raised by Radjavi. In section 2, we generalize some results in section 1 tothe case of reductive algebras. Section 3 discusses the commutant of a reductive algebra and gives