  We provide a general operator algebraic formulation of superfluidity in Bose
systems, with the aim of investigating the relationships of this phenomenon
both to off-diagonal long range order (ODLRO) and to a mathematically precise
version of Landau's picture of elementary excitations. Our principal results
are that ODLRO leads both to rotational superfluidity and to Goldstone
excitations, while the neo-Landau picture accounts for the translational
superfluidity of flow along a pipe. The latter picture is realised by the
Lieb-Liniger-Girardeau model. Open problems are briefly discussed.
