Geodesic
Weak Convergence Is Not Strong Convergence For Amenable Groups
Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 231-241

Voir la notice de l'article provenant de la source Cambridge University Press

Let $G$ be an infinite discrete amenable group or a non-discrete amenable group. It is shown how to construct a net $\left( {{f}_{\alpha }} \right)$ of positive, normalized functions in ${{L}_{1}}\left( G \right)$ such that the net converges weak* to invariance but does not converge strongly to invariance. The solution of certain linear equations determined by colorings of the Cayley graphs of the group are central to this construction.
DOI : 10.4153/CMB-2001-023-x
Mots-clés : 43A07 
Rosenblatt, Joseph M.; Willis, George A. Weak Convergence Is Not Strong Convergence For Amenable Groups. Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 231-241. doi: 10.4153/CMB-2001-023-x
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