G. Racher
On Injective Von Neumann Algebras
Preprint series: ESI preprints

MSC:

46L10 General theory of von Neumann algebras

46L05 General theory of $C$*-algebras

46M10 Projective and injective objects, See also {46A22}

Abstract: Supplementing the work 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.


Keywords: Injective von Neumann algebras, nuclear $C^{*}$-algebras, injective Banach modules