A note on 𝑀-ideals in 𝐵(𝑋)

Abstract

In this paper we prove some properties of M-ideals and HB-subspaces in an arbitrary Banach space. We then apply these properties to prove a theorem which generalizes to other spaces Smith’s and Ward’s results in [8]: for 1 > p > ∞ , B ( l p ) 1 > p > \infty ,B({l_p}) contains no nontrivial summands and that each nontrivial M-ideal in B ( l p ) B({l_p}) contains K ( l p ) K({l_p}) .