- This paper is concerned with the M-ideal structure of the algebras B(lp) of bounded operators on the sequence spaces lp1 < p < . The M-summands are completely determined, but the M-ideals are only partially characterized. However evidence is presented to support the conjecture that the only nontrivial M-ideal is the ideal C(lp) of compact operators on lp. 1979, University of California, Berkeley. All Rights Reserved.