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Paschke's conjecture for the endpoint anisotropic series representations of the free group

Part of: Structure and classification of infinite or finite groups Locally compact groups and their algebras

Published online by Cambridge University Press:  09 April 2009

M. Gabriella Kuhn  and
Tim Steger
M. Gabriella Kuhn
Affiliation:
Dipartimento di Matematica Università di Milano “Bicocca”Viale Sarca 202 20126 MilanoItalia e-mail: kuhn@matapp.unimib.it
Tim Steger
Affiliation:
Struttura di Matematica e Fisica Università di SassariVia Vienna 2 07100 SassariItalia e-mail: steger@ssmain.uniss.it
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Abstract

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Let Γ be a free noncommutative group with free generating set A+. Let μ ∈ ℓ1(Γ) be real, symmetric, nonnegative and suppose that supp. Let λ be an endpoint of the spectrum of μ considered as a convolver on ℓ2(Γ). Then λ − μ is in the left kernel of exactly one pure state of the reduced in particular, Paschke's conjecture holds for λ − μ.

Keywords

free groupirreducible unitary representationpure state.

MSC classification

Secondary: 20E05: Free nonabelian groups 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 173 - 184
Copyright
Copyright © Australian Mathematical Society 2003

References

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