  We extend a localization result for the $H^{1/2}$ norm by B. Faermann to a
wider class of subspaces of $H^{1/2}(\Gamma)$, and we prove an analogous result
for the $H^{-1/2}(\Gamma)$ norm, $\Gamma$ being the boundary of a bounded
polytopal domain $\Omega$ in $\mathbb{R}^n$, $n=2,3$. As a corollary, we obtain
equivalent, better localized, norms for both $H^{1/2}(\Gamma)$ and
$H^{-1/2}(\Gamma)$, which can be exploited, for instance, in the design of
preconditioners or of stabilized methods.
