A Liouville Space, also known as line space or "extended" Hilbert space, it is the Cartesian product of two Hilbert spaces.
Liouville Space
See also
Cartesian Product, Hilbert SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Liouville Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LiouvilleSpace.html