On positivity of the Kadison constant and noncommutative Bloch theory

Varghese Mathai

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On positivity of the Kadison constant and noncommutative Bloch theory

Varghese Mathai

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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.

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Varghese Mathai. 2001-05-06. On positivity of the Kadison constant and noncommutative Bloch theory. https://arxiv.org/abs/math/0010309

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