Shrinking and boundedly complete Schauder frames in Fréchet spaces |
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| Authors: | José Bonet,Carmen Ferná ndez,Antonio Galbis,Juan M. Ribera |
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| Affiliation: | 1. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, E-46071 València, Spain;2. Departamento de Análisis Matemático, Universitat de València, E-46100 Burjassot, València, Spain |
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| Abstract: | 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. |
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| Keywords: | Atomic decomposition Schauder basis Schauder frame Fré chet spaces (LB)-spaces Reflexivity Locally convex spaces Shrinking Boundedly complete |
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