  A reflexive hereditarily indecomposable Banach space
$\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$ infinite
dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$ and every
bounded linear operator $T:Y\rightarrow Y$, the operator $T$ admits a
non-trivial closed invariant subspace.
