6533b85dfe1ef96bd12be88e

RESEARCH PRODUCT

Shrinking and boundedly complete Schauder frames in Fréchet spaces

Carmen FernandezJuan Miguel Ribera PuchadesJose BonetAntonio GalbisJosep-maria Ribera

subject

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsShrinkingReflexivitySchauder basisFunction space(LB)-spacesApplied MathematicsMathematics::Analysis of PDEsConvex setMathematics::General TopologyFréchet spacesSchauder basisAtomic decompositionSchauder fixed point theoremSchauder frameLocally convex spacesLocally convex topological vector spaceBoundedly completeDual polyhedronAtomic decompositionMATEMATICA APLICADAAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2014-02-01
10.1016/j.jmaa.2013.09.010https://hdl.handle.net/10251/38326