$\textbf{Hahn Banach theorem for normed spaces}$
Let $U$ be a subspace of a normed space $X$. For every bounded linear functional $u^*:U\to\mathbb{F}$ there exists a bounded linear functional $x^*:X\to\mathbb{F}$ such that $\lVert x^*\rVert=\lVert u^*\rVert$ and the restriction of $x^*$ to $U$ is $u^*$. That is, $u^*$ can be extended to a bounded linear functional on $X$ having the same norm.
$\textbf{Hahn Banach theorem for normed spaces}$
Let $U$ be a subspace of a normed space $X$. For every bounded linear functional $u^*:U\to\mathbb{F}$ there exists a bounded linear functional $x^*:X\to\mathbb{F}$ such that $\lVert x^*\rVert=\lVert u^*\rVert$ and the restriction of $x^*$ to $U$ is $u^*$. That is, $u^*$ can be extended to a bounded linear functional on $X$ having the same norm.
copied
๐๐๐ก๐งย ๐๐๐ง๐๐๐กย ๐ญ๐ก๐๐จ๐ซ๐๐ฆย ๐๐จ๐ซย ๐ง๐จ๐ซ๐ฆ๐๐ย ๐ฌ๐ฉ๐๐๐๐ฌ
Let ๐ be a subspace of a normed space ๐. For every bounded linear functional ๐ข*:๐โ๐ฝ there exists a bounded linear functional ๐ฅ*:๐โ๐ฝ such that โฅ๐ฅ*โฅ=โฅ๐ข*โฅ and the restriction of ๐ฅ* to ๐ is ๐ข*. That is, ๐ข* can be extended to a bounded linear functional on ๐ having the same norm.