Linear Interpolation and the Elementary Operators on ■

Let■be a Banach space.In this paper the sufficient and necessary condi-tions for an elementary operator on ■to be of finite rank or of rank one are obtained;a characterization of an abstract linear mapping on■to be a finite-rank elementaryoperator is given;and it is also shown that a linear interpolation of finitely many elemen-tary operators △,…,△is still an elementary operator though it may not be a linear combi-nation of △’s.