Shrinking and boundedly complete Schauder frames in Fréchet spaces

  1. Bonet, J. 1
  2. Fernández, C. 2
  3. Galbis, A. 2
  4. Ribera, J.M. 1
  1. 1 Universidad Politécnica de Valencia
    info

    Universidad Politécnica de Valencia

    Valencia, España

    ROR https://ror.org/01460j859

  2. 2 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2014

Volumen: 410

Número: 2

Páginas: 953-966

Tipo: Artículo

DOI: 10.1016/J.JMAA.2013.09.010 SCOPUS: 2-s2.0-84885329927 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

Resumen

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames 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 Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented. © 2013 Elsevier Inc.