Kirchberg's factorization property for locally compact groups

A locally compact group G has the factorization property if map C ⁎ ( ) ⊙ ∋ a ⊗ b ↦ λ ρ ∈ B L 2 is continuous with respect to minimal C*-norm. This paper seeks initiate rigorous study of this in case groups which, contrast discrete case, been relatively untouched. partial solution question when passes embeddings given – that traces back Kirchberg's seminal work on topic and known be false general. It also shown every “residually amenably embeddable” must necessarily have an analogue characterization for (T) holds more general class groups.