$\textbf{Dual space}$
Let $X$ be a normed space. The dual space of $X$ is the vector space $\mathcal{B}(X,\mathbb{F})$ of all bounded linear functionals on $X$ with the operator norm $\lVert x^*\rVert=\sup_{\lVert x\rVert\leq1}\lvert x^*(x)\rvert$. The dual space is denoted by $X^*$.
Note: The dual space $X^*$ is always a Banach space.
$\textbf{Dual space}$
Let $X$ be a normed space. The dual space of $X$ is the vector space $\mathcal{B}(X,\mathbb{F})$ of all bounded linear functionals on $X$ with the operator norm $\lVert x^*\rVert=\sup_{\lVert x\rVert\leq1}\lvert x^*(x)\rvert$. The dual space is denoted by $X^*$.
Note: The dual space $X^*$ is always a Banach space.
copied
𝐃𝐮𝐚𝐥 𝐬𝐩𝐚𝐜𝐞
Let 𝑋 be a normed space. The dual space of 𝑋 is the vector space ℬ(𝑋,𝔽) of all bounded linear functionals on 𝑋 with the operator norm ∥𝑥*∥=supⲓⲓₓⲓⲓ≤₁∣𝑥*(𝑥)∣. The dual space is denoted by 𝑋*.
Note: The dual space 𝑋* is always a Banach space.