Paper detail

Shrinking and boundedly complete atomic decompositions in Fréchet spaces

We study atomic decompositions in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete atomic decompositions on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional atomic decomposition is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete atomic decompositions in function spaces are also presented.