Discontinuous Translation Invariant Functionals

DOI10.2307/1999595zbMath0537.43002OpenAlexW4254947025MaRDI QIDQ3322593

Sadahiro Saeki

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999595

zbMATH Keywords

amenableconvolution measure algebradiscontinuous translation invariant functionalsLebesgue spaces \(L^ p\)

Mathematics Subject Classification ID

(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Measure algebras on groups, semigroups, etc. (43A10)

Related Items (8)

Invariant functionals and the uniqueness of invariant norms ⋮ Continuity of translation invariant linear functionals on \(C_ 0(G)\) for certain locally compact groups G ⋮ Translation-invariant linear forms on \({\mathcal E}'(G)\) and non-Liouville tuples on G ⋮ Automatic continuity of perturbations of casual operators ⋮ Translation invariant linear functionals on segal algebras ⋮ Uniqueness of translation invariant norms ⋮ Uniqueness of norm on \(L^{p}(G)\) and \(C(G)\) when \(G\) is a compact group. ⋮ Linear maps determining the norm topology

Cites Work

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• On the invariant mean on topological semigroups and on topological groups
• Translation-invariant linear forms and a formula for the Dirac measure
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• Some discontinuous translation-invariant linear forms
• Translation-Invariant Functionals
• Different Types of Invariant Means
• Continuity of Operators on L ₂ (G ) and L ₁ (G ) Commuting with Translations
• The Exact Cardinality of the Set of Invariant Means on a Group
• The Ranges of Certain Convolution Operators.
• On left amenable semigroups which admit countable left invariant means
• Invariant means on $L^{∞}$
• A Guichard theorems on connected monothetic groups

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