Gâteaux differentiable points with special representation
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- by Seung Jae Oh PDF
- Proc. Amer. Math. Soc. 93 (1985), 456-458 Request permission
Abstract:
If $({x_n})$ is a bounded sequence in a Banach space, is there an element $x = \sum \nolimits _{n = 1}^\infty {{a_n}{x_n}}$ sucn that $\sum \nolimits _{n = 1}^\infty {\left \| {{a_n}{x_n}} \right \| < \infty }$ and tne directional derivative of the norm at $x$, $D(x,{x_n})$, exists for every $n$? In fact, there are such $x$’s dense in the closed span of $\left \{ {{x_n}} \right \}$. An application of this fact is made to a proof of Rybakov’s theorem on vector measures.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 456-458
- MSC: Primary 46G05; Secondary 46A99, 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0774002-1
- MathSciNet review: 774002