### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Functional Analysis*,

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

**Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras.** / Archbold, Robert J; Kaniuth, Eberhard; Somerset, Douglas W B.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 262, no. 5, pp. 2050-2073. https://doi.org/10.1016/j.jfa.2011.12.015

}

TY - JOUR

T1 - Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras

AU - Archbold, Robert J

AU - Kaniuth, Eberhard

AU - Somerset, Douglas W B

N1 - Acknowledegments The authors are grateful to the London Mathematical Society for grant number 4919 which partially supported this research.

PY - 2012/3/1

Y1 - 2012/3/1

N2 - 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.

AB - 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.

KW - C⁎-algebra

KW - multiplier algebra

KW - inner derivation

KW - norm

KW - ideal space and topology

KW - graph structure

KW - locally compact group

KW - Group C⁎-algebra

U2 - 10.1016/j.jfa.2011.12.015

DO - 10.1016/j.jfa.2011.12.015

M3 - Article

VL - 262

SP - 2050

EP - 2073

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 5

ER -