Discontinuous translation invariant functionals
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- by Sadahiro Saeki PDF
- Trans. Amer. Math. Soc. 282 (1984), 403-414 Request permission
Abstract:
Let $G$ be an infinite $\sigma$-compact locally compact group. We shall study the existence of many discontinuous translation invariant linear functionals on a variety of translation invariant FrΓ©chet spaces of Radon measures on $G$. These spaces include the convolution measure algebra $M(G)$, the Lebesgue spaces ${L^p}(G)$, where $1 \leq p \leq \infty$, and certain combinations thereof. Among other things, it will be shown that $C(G)$ has many discontinuous translation invariant functionals, provided that $G$ is amenable. This solves a problem of G. H. Meisters.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 403-414
- MSC: Primary 43A15; Secondary 43A05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0728720-5
- MathSciNet review: 728720