Keyword: Leinert Sets : Search

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Search name	Searched On	Run search
Keyword: Nb2o5-dopant (3)	1 Apr 2025	Run
Keyword: Leinert Sets (1)	1 Apr 2025	Run
Keyword: Louvered Fin (2)	1 Apr 2025	Run
Keyword: Heating Time (3)	1 Apr 2025	Run
Keyword: Gabor System (2)	1 Apr 2025	Run

articleNo Access
A computational approach to the Thompson group F
International Journal of Algebra and Computation09 Apr 2015
Preview Abstract
Let F denote the Thompson group with standard generators A = x₀, B = x₁. It is a long standing open problem whether F is an amenable group. By a result of Kesten from 1959, amenability of F is equivalent to
and to
where in both cases the norm of an element in the group ring ℂF is computed in B(ℓ²(F)) via the regular representation of F. By extensive numerical computations, we obtain precise lower bounds for the norms in (i) and (ii), as well as good estimates of the spectral distributions of (I+A+B)*(I+A+B) and of A+A^-1+B+B^-1 with respect to the tracial state τ on the group von Neumann Algebra L(F). Our computational results suggest, that
It is however hard to obtain precise upper bounds for the norms, and our methods cannot be used to prove non-amenability of F.

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