𝑀-structure in the Banach algebra of operators on 𝐶₀(Ω)

Flinn, P. H.; Smith, R. R.

doi:10.1090/S0002-9947-1984-0719668-0

$M$-structure in the Banach algebra of operators on $C_{0}(\Omega )$
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by P. H. Flinn and R. R. Smith

Trans. Amer. Math. Soc. 281 (1984), 233-242

DOI: https://doi.org/10.1090/S0002-9947-1984-0719668-0

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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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