English

On positivity of the Kadison constant and noncommutative Bloch theory

Differential Geometry 2007-05-23 v3

Abstract

In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in noncommutative Bloch theory on the non-existence of Cantor set type spectrum. This is accomplished by establishing an explicit lower bound for the Kadison constant of twisted group C*-algebras in a large number of cases, whenever the multiplier is rational.

Keywords

Cite

@article{arxiv.math/0010309,
  title  = {On positivity of the Kadison constant and noncommutative Bloch theory},
  author = {Varghese Mathai},
  journal= {arXiv preprint arXiv:math/0010309},
  year   = {2007}
}

Comments

Latex2e, 16 pages, final version, to appear in a special issue of Tohoku Math. J. (in press)