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

作者：Archbold Robert J^*; Kaniuth Eberhard; Somerset Douglas W B

来源：Journal of Functional Analysis, 2012, 262(5): 2050-2073.

DOI：10.1016/j.jfa.2011.12.015

• C*-algebra
• Multiplier algebra
• Inner derivation
• Norm
• Ideal space and topology
• Graph structure
• Locally compact group
• Group C*-algebra

The derivation constant K (A) %26gt;= 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)) %26lt;= 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.

• 出版日期2012-3-1