Duality, reflexivity and atomic decompositions in Banach spaces

• Autorzy: Daniel Carando , Silvia Lassalle
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 46B10: Duality and reflexivity
• 42C15: General harmonic expansions, frames
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 1
• Strony: 67-80

Daty

wydano

2009

Twórcy

autor

Daniel Carando

• Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
• CONICET

autor

Silvia Lassalle

• Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
• CONICET

Identyfikatory

DOI

10.4064/sm191-1-5