deficiency indices

Question

Let the deficiency indices of a closed symmetric operator $A$ be $$n_+ = ker(A^*-iI), n_- = ker(A^*+iI)$$ and $A$ can be expanded to be self-adjoint iff $n_+ = n_-$, even if both indices is (countably) infinity. My question is, is this holds with uncountably infinity? And what if one is countable but the other isn't? Thanks for help!