1 results
Paschke's conjecture for the endpoint anisotropic series representations of the free group
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 74 / Issue 2 / April 2003
- Published online by Cambridge University Press:
- 09 April 2009, pp. 173-184
- Print publication:
- April 2003
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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.
. Let λ be an endpoint of the spectrum of μ considered as a convolver on ℓ
in particular, Paschke's conjecture holds for λ − μ.