Infinite type power series subspaces of finite type power series spaces

Nuclear power series spaces of finite type, Λ₀(α), and infinite type, Λ_∞(α), are considered. Sufficient conditions are given on α for which there exists a β such that Λ_∞(β) is isomorphic to a subspace of Λ₀(α) and also for which there does not exist such a β. In certain cases it is possible to take β=α. The results in this paper are related to earlier results by S. Rolewicz and V. P. Zaharyuta.