A very natural example of a nuclear Montel space is the space $H(D)$ of all holomorphic functions on the open disc topologized by the family of seminorms

$$p_n(f)=\sup\{|f(z)|\colon |z|\leq 1-\tfrac{1}{n}\},\, n\in \mathbb N, f\in H(D) $$

I cannot find any good references concerning this space. In particular, I have two following questions:

1) Can one give examples of subspaces of $H(D)$ which are not isomorphic to it?

2) Does every copy of $H(D)$ contain further complemented one?

Thank you in advance.