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A note on generalized characters

S J Bhatt·H V Dedania
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Abstract

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 $H(G) = \dg$ (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 $\ccg$ equipped with the inductive limit topology is topologically homeomorphic to $\hg$.

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S J Bhatt, H V Dedania. 2005-12-14. A note on generalized characters. https://arxiv.org/abs/math/0512317

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