Weak compactness in the dual of a \(C^*\)-algebra is determined commutatively
We prove Pelczyński's property (V) for \(C^*\)-algebras by proving that weak compactness in the dual of a \(C^*\)-algebra is determined commutatively. Thus von Neumann algebras -- and in particular \(L(H)\) -- are Grothendieck spaces.
Pelczyński's property (V) for \(C^*\)-algebras
weak compactness in the dual of a \(C^*\)-algebra is determined commutatively
scientific article; zbMATH DE number 537321
scientific article