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Translation-invariant linear forms on $ L\sb p(G)$

Author: Joseph Rosenblatt
Journal: Proc. Amer. Math. Soc. 94 (1985), 226-228
MSC: Primary 43A15
MathSciNet review: 784168
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Abstract: Let $ G$ be a compact group such that the identity representation of $ G$ is not contained in the regular representation on $ L_2^0(G,{\lambda _G})$ of $ G$ with the discrete topology. Then any left translation invariant linear form on $ {L_p}(G),1 < p < \infty $, is continuous and must be a constant times the Haar integral. This shows that many classical matrix groups $ G$ admit only continuous left translation invariant linear forms on $ {L_p}(G),1 < p < \infty $.

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