Given operators $X$ and $Y$ acting on a Hilbert space $mathcal H$, an interpolating operator is a bounded operator $A$ such that $AX=Y$. In this article, we investigate unitary operator interpolation problems in Alg$mathcal L$ : Given operators $X$ and $Y$ acting on $mathcal H$, when does there exist a unitary operator $A$ in Alg$mathcal L$ such that $AX=Y$.

Keywords: unitary operator, unitary interpolation problem, subspace lattice, Alg$mathcal L$