Alireza Najafizadeh - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷ Tehran, Iran.
Fatemeh Karimi - Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷ Tehran, Iran.

Let V be a real or complex locally convex vector space and Lc(V ) be the ring of continuouslinear operators on V: In this talk, some results related to the characterization and propertiesof one-sided ideals of the ring Lc(V ) which have been obtained over the past decades arereviewed. Moreover, some outlines for the continuation of the subject under investigation ispresented.

linear continuous operator, ring, topological triangularizability