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A note on reflexivity in Banach spaces

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Abstract

For any normed spaceX, the unit ball ofX is weak *-dense in the unit ball ofX **. This says that for any ε>0, for anyF in the unit ball ofX **, and for anyf 1,…,f n inX *, the system of inequalities |f i(x)−F(f i)|≤ε can be solved for somex in the unit ball ofX. The author shows that the requirement that ε be strictly positive can be dropped only ifX is reflexive.

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Pavone, M. A note on reflexivity in Banach spaces. Rend. Circ. Mat. Palermo 37, 120–125 (1988). https://doi.org/10.1007/BF02844272

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  • DOI: https://doi.org/10.1007/BF02844272

1980 Mathematics Subject Classification

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