On positivity of the Kadison constant and noncommutative Bloch theory

Details On positivity of the Kadison constant and noncommutative Bloch theory On positivity of the Kadison constant and noncommutative Bloch theory

2000-10-30

arxiv.org/abs/math/0010309v3

Tohoku Math. Publ., 20 (2001) 107-124

Mathematics

Differential Geometry

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

Scientific paper

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.

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