Gâteaux differentiable points with special representation
Seung Jae Oh
Proc. Amer. Math. Soc. 93 (1985), 456-458
Primary 46G05; Secondary 46A99, 46G10
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Abstract: If is a bounded sequence in a Banach space, is there an element sucn that and tne directional derivative of the norm at , , exists for every ? In fact, there are such 's dense in the closed span of . An application of this fact is made to a proof of Rybakov's theorem on vector measures.
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- J. Diestel and J. J. Uhl, Jr., Vector measures, Amer. Math. Soc., Providence, R. I., 1970. MR 0453964 (56:12216)
- J. R. Giles, Convex analysis with application in differentiation of convex functions, Pitman, Boston. Mass., 1982. MR 650456 (83g:46001)
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- V. Rybakov, Theorem of Bartle, Dunford, and Schwartz on vector- valued measures, Mat. Zametki 7 (1970), 247-254. MR 0260971 (41:5591)
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