### Abstract

The derivation constant K (A) ≥ 1/2 has been previously studied for unital non-commutative C*- algebras A. This paper begins the study of K(M(A)) where M (A) is the multiplier algebra of a non-unital C*-algebra A. Two results are obtained giving separate conditions on A which imply that K(M(A)) ≤ 1.These results are applied to A=C* (G)for a number of locally compact groups G including SL(2,R), SL (2,C)and several 2-step solvable groups. In these cases, K (M(A))=1. On the other hand, if G is a (non-abelian) amenable [SIN]-group then K (M(A))=1/2.

Original language | English |
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Pages (from-to) | 2050-2073 |

Number of pages | 24 |

Journal | Journal of Functional Analysis |

Volume | 262 |

Issue number | 5 |

Early online date | 29 Dec 2011 |

DOIs | |

Publication status | Published - 1 Mar 2012 |

### Keywords

- C⁎-algebra
- multiplier algebra
- inner derivation
- norm
- ideal space and topology
- graph structure
- locally compact group
- Group C⁎-algebra

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## Cite this

Archbold, R. J., Kaniuth, E., & Somerset, D. W. B. (2012). Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras.

*Journal of Functional Analysis*,*262*(5), 2050-2073. https://doi.org/10.1016/j.jfa.2011.12.015