We have $Y=\bar(span)\{e_n: n \geq 1\}$, which is a closed convex subspace of a strictly convex reflexive Hilbert space with an equivalent norm, where $e_n=(0,...,1,0...)$, 1 in the n-th place. It is clear that $Y$ is weakly strongly Chebyshev subspace. But can we find a best approximation of the closed unit ball of $Y$? i.e., will $B_Y$ become proximinal set?