Hypo-EP Operators And Compact Pertubations

A bounded linear operator T acting on a Hilbert space is called EP operator if ran(T)is closed and ran(T)=ran(T*).A bounded linear operator T acting on a Hilbert space is called Hypo-EP operator if ran(T)is closed and ran(T)(?)ran(T*).In this paper,we investigate the compact pertubations of operators with Hypo-EP property.We characterize those operators for which has arbitrarily small compact per-tubations to have Hypo-EP property.Also,we study the stability of these properties under small compact pertubations.