Translation invariant functionals on Lp (G) when G is not amenable

Journal of the Australian Mathematical Society

G. A. Willis¹ 

关键词: 43 A 07;   

DOI  :  10.1017/S1446788700033656

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown