# Journal of Operator Theory

Volume 40, Issue 1, Summer 1998 pp. 3-34.

A decomposition theorem for operators on $L^1$**Authors**: Zhuxing Liu

**Author institution:**Department of Mathematics, Hebei University of Technology, Tianjin, P.R. China

**Summary:**The operator space $\L(L^1)$, as a Banach lattice, can be decomposed into four bands: the Radon-Nikodym band, the Dunford-Pettis band, the Rosenthal band, and the Enflo band. Thus, each operator in $\LL$ can be decomposed uniquely into the sum of four operators, so that each member of the decomposition has a characterization in terms of natural videly discussed operator-theoretic invariants in Banach space theory.

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