A note on 𝑀-ideals in 𝐵(𝑋)

Hennefeld, Julien

doi:10.1090/S0002-9939-1980-0548090-7

A note on $M$-ideals in $B(X)$
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Proc. Amer. Math. Soc. 78 (1980), 89-92 Request permission

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 $1 < p < \infty ,B({l_p})$ contains no nontrivial summands and that each nontrivial M-ideal in $B({l_p})$ contains $K({l_p})$.

References

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Julien Hennefeld, A decomposition for $B(X)^{\ast }$ and unique Hahn-Banach extensions, Pacific J. Math. 46 (1973), 197–199. MR 370265, DOI 10.2140/pjm.1973.46.197

as a subspace of

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M-ideals in