Some generalizations of ascent and descent for linear operators

Abstract The purpose of this paper is to present in linear spaces some results for new notions called A -left (resp., -right) ascent and descent operators (where a given operator) which generalize two important operator theory: descent. Moreover, if positive operator, we obtain several properties an semi-Hilbertian spaces. Some basic many related the on space Kaashoek (Math Ann 172:105–115, 1967), Taylor 163:18–49, 1966) are extended these notions. stability under perturbations by compact having finite rank power also