## Abstract

We consider a properly converging sequence of non-characters in the dual space of a thread-like group G_{N} (N≥3}) and investigate the limit set and the strength with which the sequence converges to each of its limits. We show that, if (π _{k} ) is a properly convergent sequence of non-characters in ĜN, then there is a trade-off between the number of limits σ which are not characters, their degrees, and the strength of convergence i _{σ} to each of these limits (Theorem 3.2). This enables us to describe various possibilities for maximal limit sets consisting entirely of non-characters (Theorem 4.6). In Sect. 5, we show that if (π _{k} ) is a properly converging sequence of non-characters in ĜN and if the limit set contains a character then the intersection of the set of characters (which is homeomorphic to Rdbl; ) with the limit set has at most two components. In the case of two components, each is a half-plane. In Theorem 7.7, we show that if a sequence has a character as a cluster point then, by passing to a properly convergent subsequence and then a further subsequence, it is possible to find a real null sequence (c _{k} ) (with c _{κ}≠ 0) such that, for a in the Pedersen ideal of C *(G _{N}), lim _{k→∞}exists (not identically zero) and is given by a sum of integrals over ℝ.

Originalsprache | Englisch |
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Seiten (von - bis) | 245-282 |

Seitenumfang | 38 |

Fachzeitschrift | Mathematische Zeitschrift |

Jahrgang | 255 |

Ausgabenummer | 2 |

DOIs | |

Publikationsstatus | Veröffentlicht - Feb. 2007 |