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) ≥ 1 2 has been extensively studied for unital noncommutative 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 ∗ (GN ) where GN is the motion group R N o SO(N). Utilising the rich topological structure of the unitary dual GdN , it is shown that, for N ≥ 3, K(M(C ∗ (GN ))) = 1 2 ⌈ N 2 ⌉
Original languageEnglish
Pages (from-to)225-255
Number of pages31
JournalAdvances in Mathematics
Volume280
Early online date15 May 2015
DOIs
Publication statusPublished - 6 Aug 2015

Keywords

  • C∗-algebra
  • multiplier algebra
  • derivation
  • motion group
  • unitary dual
  • graph structure

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