A remark on discontinuous translation invariant functionals on \(L_ p (G)\) for certain compact groups \(G\) (Q1207656)
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scientific article; zbMATH DE number 164916
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on discontinuous translation invariant functionals on \(L_ p (G)\) for certain compact groups \(G\) |
scientific article; zbMATH DE number 164916 |
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A remark on discontinuous translation invariant functionals on \(L_ p (G)\) for certain compact groups \(G\) (English)
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12 May 1993
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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)].
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compact metrizable groups
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translation-invariant functionals
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