This is an announcement for the paper "Shrinking and boundedly complete atomic decompositions in Fr'echet spaces" by Jose Bonet, Carmen Fernandez, Antonio Galbis, and Juan M. Ribera.

Abstract: We study atomic decompositions in Fr'echet 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.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 46A04, secondary: 42C15

Submitted from: antonio.galbis@uv.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1212.0969

or

http://arXiv.org/abs/1212.0969