  A definition of the Schmidt number of a state of an infinite dimensional
bipartite quantum system is given and properties of the corresponding family of
Schmidt classes are considered. The existence of states with a given Schmidt
number such that any their countable convex decomposition does not contain pure
states with finite Schmidt rank is established.
  Partially entanglement breaking channels in infinite dimensions are studied.
Several properties of these channels well known in finite dimensions are
generalized to the infinite dimensional case. At the same time, the existence
of partially entanglement breaking channels (in particular, entanglement
breaking channels) such that all operators in any their Kraus representations
have infinite rank is proved.
