If $X$ is a Banach space admitting a Schauder basis, then can we choose a set $\{e_1,e_2,e_3 \cdots \}$ as the basis such that there are bounded linear functional $f_i$ such that $f_i(e_j)=\delta_{ij}$?

Let $V$ be a vector space with infinite dimensions. A Hamel basis for $V$ is an ordered set of linearly independent vectors $\{ v_i \ | \ i \in I\}$ such that any $v \in V$ can be expressed as a finite linear combination of the $v_i$’s; so $\{ v_i \ | \ i \in […]

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