A remark on discontinuous translation invariant functionals on \(L_ p (G)\) for certain compact groups \(G\)
The authors exhibit a class of compact metrizable non-abelian groups with the property that there exist discontinuous translation-invariant functionals on \(C(G)\) and \(L_ p(G)\) for \(1 \leq p \leq \infty\). This extends and complements results of \textit{G. H. Meisters} and \textit{W. M. Schmidt} [J. Funct. Anal. 11, 407-424 (1972; Zbl 0247.43004)] and \textit{B. E. Johnson} [Bull. Sci. Math., II. Sér. 107, 301-310 (1983; Zbl 0529.43003)].
scientific article; zbMATH DE number 164916