Complemented infinite type power series subspaces of nuclear Fréchet spaces (Q1101920)

It is proved, that a complemented subspace E with stable diametral dimension of a nuclear power series space has a basis. This result applies for example to \({\mathcal O}(M)\), the space of analytic functions on a d-dimensional Stein manifold M, and it is shown, that \({\mathcal O}(M)\) is isomorphic to \({\mathcal O}({\mathbb{C}}^ d)\) iff every bounded, plurisubharmonic function on M is constant. The proof is based on the contruction of a complemented subspace of E, which is isomorphic to the space \(\Lambda _{\infty}(\alpha)\) given by the diametral dimension of E, and the power series space decomposition result of Vogt (``Pelczynski's trick'').