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A note on $ M$-ideals in $ B(X)$


Author: Julien Hennefeld
Journal: Proc. Amer. Math. Soc. 78 (1980), 89-92
MSC: Primary 46B20; Secondary 47D30
DOI: https://doi.org/10.1090/S0002-9939-1980-0548090-7
MathSciNet review: 548090
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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})$.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0548090-7
Keywords: M-ideals, basis, compact operators
Article copyright: © Copyright 1980 American Mathematical Society

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