Geometric properties of Fréchet spaces and selection of basis sequences (Q1972546)

The existence of a basis for a nuclear Fréchet space having certain geometric properties is shown. The approach consists of showing that a space with these properties is isomorphic to a complemented subspace of the ``universal'' nuclear Fréchet space \(s\), from which an intricate construction allows the application of known results concerning the existence of a basis in a complemented subspace of \(s\) to give the desired conclusion.