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Results tagged with banach-spaces
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user 32507
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
3
votes
Accepted
Subgradient in a predual under weak* continuity
Finally, I was able to cook up a counterexample. We choose $X = c_0$ (zero sequences equipped with supremum norm). Thus, the dual spaces are (isometric to) $X^* = \ell^1$ and $X^{**} = \ell^\infty$.
W …
- 1,724
1
vote
Necessary conditions for optimality in Banach spaces
Let us assume that your $f$ is at least directionally differentiable at $x_0$ and that the directional derivative depends continuously on the direction (this may be satisfied under rather general assu …
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