Geodesic
Duality, reflexivity and atomic decompositions in Banach spaces
Daniel Carando1 ; Silvia Lassalle1
1Departamento de Matemática - Pab I Facultad de Cs. Exactas y Naturales Universidad de Buenos Aires (1428) Buenos Aires, Argentina and CONICET
Studia Mathematica, Tome 191 (2009) no. 1, pp. 67-80
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We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking” and “boundedly complete” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions.
DOI : 10.4064/sm191-1-5
Keywords: study atomic decompositions their relationship duality reflexivity banach spaces end extend concepts shrinking boundedly complete schauder basis atomic decomposition framework allows answer basic duality question atomic decomposition banach space generates duality atomic decomposition its dual space characterize reflexivity banach space terms properties its atomic decompositions

Daniel Carando  1   ; Silvia Lassalle  1

1 Departamento de Matemática - Pab I Facultad de Cs. Exactas y Naturales Universidad de Buenos Aires (1428) Buenos Aires, Argentina and CONICET 
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Daniel Carando; Silvia Lassalle. Duality, reflexivity and atomic decompositions
 in Banach spaces. Studia Mathematica, Tome 191 (2009) no. 1, pp. 67-80. doi: 10.4064/sm191-1-5

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