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Translation invariant functionals on Lp (G) when G is not amenable
Published online by Cambridge University Press: 09 April 2009
Abstract
It is shown that if G is a non-amenable group, then there are no non-zero translation invariant functionals on Lp(G) for 1 < p < ∞. Furthermore, if G contains a closed, non-abelian free subgroup, then there are no non-zero translation invariant functionals on C0(G). The latter is proved by showing that a certain non-invertible convolution operator on C0(G) is surjective.
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- Copyright © Australian Mathematical Society 1986
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