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

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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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     author = {Rosenblatt, Joseph M. and Willis, George A.},
     title = {Weak {Convergence} {Is} {Not} {Strong} {Convergence} {For} {Amenable} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {231--241},
     year = {2001},
     volume = {44},
     number = {2},
     doi = {10.4153/CMB-2001-023-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-023-x/}
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