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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ M$-structure in the Banach algebra of operators on $ C\sb{0}(\Omega )$


Authors: P. H. Flinn and R. R. Smith
Journal: Trans. Amer. Math. Soc. 281 (1984), 233-242
MSC: Primary 46H99; Secondary 46J99, 47D30
MathSciNet review: 719668
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Abstract: The $ M$-ideals in $ B({C_0}(\Omega ))$, the space of continuous linear operators on $ {C_0}(\Omega )$, are determined where $ \Omega $ is a locally compact Hausdorff countably paracompact space. A one-to-one correspondence between $ M$-ideals in $ B({C_0}(\Omega ))$, open subsets of the Stone-Čech compactification of $ \Omega $, and lower semicontinuous Hermitian projections in $ B{({C_0}(\Omega ))^{\ast\ast}}$ is established.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0719668-0
Keywords: $ M$-ideal, $ M$-summand, Banach algebra, Hermitian projections, lower semicontinuous projections, countably paracompact space
Article copyright: © Copyright 1984 American Mathematical Society