Let $X$ be a Banach space, and $x\in X$. Is it true that there exists $(x^*_n)$ a sequence in $X^*$ such that $\|x^*_n\| \leq 1$ and $x^*_n(x)\xrightarrow[n \to \infty]{}\|x\|$? It's true if $X$ is reflexive, but I wonder if it's true otherwise.
2026-02-23 13:28:38.1771853318
The existence of a sequence in a non reflexive Banach space
22 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in BANACH-SPACES
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