  T.-J. Li and W. Zhang defined an almost complex structure $J$ on a manifold
$X$ to be {\em \Cpf}, if the second de Rham cohomology group can be decomposed
as a direct sum of the subgroups whose elements are cohomology classes
admitting $J$-invariant and $J$-anti-invariant representatives. It turns out
(see T. Draghici, T.-J. Li and W. Zhang) that any almost complex structure on a
4-dimensional compact manifold is \Cpf. We study the $J$-invariant and
$J$-anti-invariant cohomology subgroups on almost complex manifolds, possibly
non compact. In particular, we prove an analytic continuation result for
anti-invariant forms on almost complex manifolds.
