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Weak Convergence Is Not Strong Convergence For Amenable Groups |
Canad. Math. Bull. 44(2001), 231-241
Published:2001-06-01
Printed: Jun 2001
Printed: Jun 2001
- Joseph M. Rosenblatt
- George A. Willis
Abstract
Let $G$ be an infinite discrete amenable group or a non-discrete
amenable group. It is shown how to construct a net $(f_\alpha)$ of
positive, normalized functions in $L_1(G)$ 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.
| MSC Classifications: | 43A07 - Means on groups, semigroups, etc.; amenable groups |