LINEAR INTERPOLATION AND THE ELEMENTARY OPERATORS ON B(H)

Let H be a Banach space. In this paper the sufficient and necessary conditions for an elementary operator on B(H) to be of finite rank or of rank one are obtained; a characterization of an abstract linear mapping on B(H) to be a finite-rank elementary operator is given; and it is also shown that a linear interpolation of finitely many elementary operators DELTA1,...,DELTA(k) is still an elementary operator though it may not be a linear combination of DELTA(i)'s.