B(G) is not operator Connes-amenable for non-compact locally compact groups with property (T) and finite almost periodic compactification, or for discrete groups without the factorization property.
Runde,Amenable Banach algebras
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On operator Connes-amenability of the Fourier-Stieltjes algebra
B(G) is not operator Connes-amenable for non-compact locally compact groups with property (T) and finite almost periodic compactification, or for discrete groups without the factorization property.