Solution
= Solution
A \b[<biorthogonal system>] is a family $(x_i,f_i)_{i\in I}$ with $x_i\in X$, $f_i\in X^*$, satisfying
$$
\boxed{f_i(x_j)=\delta_{ij}\quad(i,j\in I).}
$$
Thus each continuous coordinate functional takes value one on its own <vector> and zero on all others. The <vectors> need not be orthogonal in any inner product, and totality of their <linear span> is an additional condition.