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Strength of Convergence in Duals of C*-Algebras and Nilpotent Lie Groups

✍ Scribed by R.J. Archbold; E. Kaniuth; J. Ludwig; G. Schlichting; D.W.B. Somerset

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
284 KB
Volume
158
Category
Article
ISSN
0001-8708

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✦ Synopsis

By using trace formulae, the recent concept of upper multiplicity for an irreducible representation of a C*-algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent Lie group G. In particular, it is shown that if ? # G has finite upper multiplicity then this integer is the greatest strength with which a sequence in G can converge to ?. Upper multiplicities are calculated for all irreducible representations of the groups in the threadlike generalization of the Heisenberg group. The values are computed by combining new C*-theoretic results with detailed analysis of the convergence of coadjoint orbits and they show that every positive integer occurs for this class of groups.

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