Simple bounded weight modules of ${\displaystyle \mathfrak{s}\mathfrak{l}(\mathrm{\infty })}$, ${\displaystyle \mathfrak{o}(\mathrm{\infty })}$, ${\displaystyle \mathfrak{s}\mathfrak{p}(\mathrm{\infty })}$

We classify the simple bounded weight modules of $\mathfrak{s}\mathfrak{l}(\mathrm{\infty })$, $\mathfrak{o}(\mathrm{\infty })$ and $\mathfrak{s}\mathfrak{p}(\mathrm{\infty })$, and compute their annihilators in $U(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$, $U(\mathfrak{o}(\mathrm{\infty }))$, $U(\mathfrak{s}\mathfrak{p}(\mathrm{\infty }))$, respectively.