  The resolvent convergence of self-adjoint operators via the technique of
$\Gamma$-convergence of quadratic forms is adapted to incorporate complex
Hilbert spaces. As an application, we find effective operators to the Dirichlet
Laplacian with magnetic potentials in very thin bounded tubular regions in
space built along smooth closed curves; relatively weak regularity is asked for
the potentials, and the convergence is in the norm resolvent sense as the cross
sections of the tubes go uniformly to zero.
