Continuity of translation invariant linear functionals on \(C_ 0(G)\) for certain locally compact groups G

DOI10.1007/BF01501168zbMath0637.43003MaRDI QIDQ1099027

George A. Willis

Publication date: 1988

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178371

zbMATH Keywords

translation invariant linear functionalsdense subgroup with property T

Mathematics Subject Classification ID

(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (7)

Invariant functionals and the uniqueness of invariant norms ⋮ Topologically invariant linear forms on spaces of abstract distributions on a locally compact Abelian group ⋮ Functions with a Unique Mean Value and Amenability ⋮ Applications of Kazhdan's property (T) to automatic continuity ⋮ A remark on continuity of translation invariant functionals on \(L_ p(G)\) for compact Lie groups G ⋮ Continuity of operators commuting with translations for compact groups ⋮ Uniqueness of norm on \(L^{p}(G)\) and \(C(G)\) when \(G\) is a compact group.

Cites Work

• Finitely additive measures on \(S^ 2\) and \(S^ 3\), invariant with respect to rotations
• Discontinuous Translation Invariant Functionals
• Translation-Invariant Linear Forms on L p (G)
• For 𝑛>3 there is only one finitely additive rotationally invariant measure on the 𝑛-sphere defined on all Lebesgue measurable subsets
• Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
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