Let Γ be a free noncommutative group with free generating set A+. Let μ ∈ l1(Γ) be real, symmetric, nonnegative and suppose that supp(μ) = A+ ∪ A+-1. 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 C*reg (Γ); in particular, Paschke's conjecture holds for λ - μ.
Kuhn, M., Steger, T. (2003). Paschke's conjecture for the endpoint anisotropic series representations of the free group. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 74(2), 173-183 [10.1017/s1446788700003232].
Paschke's conjecture for the endpoint anisotropic series representations of the free group
KUHN, MARIA GABRIELLA;
2003
Abstract
Let Γ be a free noncommutative group with free generating set A+. Let μ ∈ l1(Γ) be real, symmetric, nonnegative and suppose that supp(μ) = A+ ∪ A+-1. 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 C*reg (Γ); in particular, Paschke's conjecture holds for λ - μ.
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