On injective von Neumann algebras

Racher, G.

doi:10.1090/S0002-9939-2010-10793-1

On injective von Neumann algebras
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Proc. Amer. Math. Soc. 139 (2011), 2529-2541 Request permission

Abstract:

Partially answering a question of A.Ya. Helemskii, we show that a von Neumann algebra is injective if and only if all its normal dual Banach left modules are $1$-injective in the sense of the homology of Banach algebras. Nuclear $C^*$-algebras are characterized in a similar manner.

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