A note on reflexivity in Banach spaces |
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Authors: | Marco Pavone |
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Institution: | 1. Department of Mathematics, University of California, 94720, Berkeley, CA
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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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