As you know, trace is linear, so trace(hk*hk'-w*w') = trace(hk*hk') - trace(w*w') .
It better be the case that only one of hk and w is a CVX variable or expression; because otherwise, the following expression is neither convex nor concave, and will not be accepted by CVX.
square_pos(norm(hk,'fro')) - square_pos(norm(w,'fro'))
If w is not a CVX variable or expression, there is no need for the reformulation of that term.
Also, if hk and w are vectors, then ,'fro' is not necessary, but does no harm.
Actually, in the expression in your first post, it better be the case that only one of hk and w is a CVX variable or expression, although it doesn’t matter which .