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

Robert J Archbold, Eberhard Kaniuth, Douglas W B Somerset

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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 languageEnglish
Pages (from-to)2050-2073
Number of pages24
JournalJournal of Functional Analysis
Issue number5
Early online date29 Dec 2011
Publication statusPublished - 1 Mar 2012



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

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