摘要
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 △<sub>1</sub>,…,△<sub>k</sub> is still an elementary operator though it may not be a linear combi-nation of △<sub>i</sub>’s.
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 elementary operator is given;and it is also shown that a linear interpolation of finitely many elemen- tary operators △_1,…,△_k is still an elementary operator though it may not be a linear combi- nation of △_i's.
基金
Project supported by the National Natural Science Foundation of China and PNSF of Shanxi
