Entanglement properties of positive operators with ranges in completely   entangled subspaces
  We prove that the projection on a completely entangled subspace S of maximum dimension in a multipartite quantum system obtained by Parthasarathy is not positive under partial transpose. We next show that several positive operators with range in S also have the same property. In this process we construct an orthonormal basis of S and provide a linking theorem to link the constructions of completely entangled subspaces due to Parthasarthy, Bhat and Johnston. 
R Sengupta, Arvind, Ajit Iqbal Singh
quant-ph math.FA