4
$\begingroup$

Let $G$ be an abelian locally compact group and $H$ be its closed subgroup. It is known from Pontryagin duality theory that every unitary character of $H$ can be extended to $G$. I think this is true for any character. Am I right? What is the reference?

$\endgroup$

1 Answer 1

4
$\begingroup$

If you mean that every continuous homomorphism $H\to\mathbf{R}$ can be extended to a continuous homomorphism $G\to\mathbf{R}$, this is contained in Theorème 5 of [1] (the "unitary" version is when $\mathbf{R}$ is replaced twice by $\mathbf{R}/\mathbf{Z}$).

[1] J. Dixmier. Quelques propriétés des groupes abéliens localement compacts. Bull. Sci. Math. (2) 81 (1957) 38-48.

$\endgroup$
1
  • $\begingroup$ Yves shot first! :-) $\endgroup$ Oct 25, 2013 at 9:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.