Norms of inner derivations for multiplier algebras of C⁎C⁎-algebras and group C⁎C⁎-algebras, II

The derivation constant K(A)≥12 has been extensively studied for unital   non-commutative C⁎C⁎-algebras. In this paper, we investigate properties of K(M(A))K(M(A)) where M(A)M(A) is the multiplier algebra of a non-unital C⁎C⁎-algebra A  . A number of general results are obtained which are then applied to the group C⁎C⁎-algebras A=C⁎(GN)A=C⁎(GN) where GNGN is the motion group RN⋊SO(N)RN⋊SO(N). Utilizing the rich topological structure of the unitary dual GNˆ, it is shown that, for N≥3N≥3,K(M(C⁎(GN)))=12⌈N2⌉.