A Note on Generalized Characters

[摘要] For a compactly generated LCA group 𝐺, it is shown that the set $H(G)$ of all generalized characters on 𝐺 equipped with the compact-open topology is a LCA group and $H(G)=hat{G}$ (the dual group of 𝐺) if and only if 𝐺 is compact. Both results fail for arbitrary LCA groups. Further, if 𝐺 is second countable, then the Gel’fand space of the commutative convolution algebra $C_c(G)$ equipped with the inductive limit topology is topologically homeomorphic to $H(G)$.

[学科分类] 数学（综合）

[关键词] Compactly generated LCA group;character;generalized character;Gel’fand space;commutative topological algebra.