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)