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

Robert J. Archbold; Eberhard Kaniuth; Douglas W. B. Somerset

doi:10.1016/j.aim.2015.04.019

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arXiv · 1504.07030

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

Robert J. Archbold·Eberhard Kaniuth·Douglas W. B. Somerset

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Abstract

The derivation constant $K(A)\geq \frac{1}{2}$ has been extensively studied for \emph{unital} non-commutative $C^*$-algebras. In this paper, we investigate properties of $K(M(A))$ where $M(A)$ is the multiplier algebra of a non-unital $C^*$-algebra $A$. A number of general results are obtained which are then applied to the group $C^*$-algebras $A=C^*(G_N)$ where $G_N$ is the motion group $\R^N\rtimes SO(N)$. Utilising the rich topological structure of the unitary dual $\widehat{G_N}$, it is shown that, for $N\geq3$, $$K(M(C^*(G_N)))= \frac{1}{2}\left\lceil \frac{N}{2}\right\rceil.$$

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Robert J. Archbold, Eberhard Kaniuth, Douglas W. B. Somerset. 2015-04-27. Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras, II. https://doi.org/10.1016/j.aim.2015.04.019

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