sentences:  For formula_6, define the Schatten p-norm of formula_3 as
  
  If formula_3 is compact and formula_10 are separable, then
  
  for formula_12
  the singular values of formula_3, i.e.the eigenvalues of the Hermitian operator formula_14.In the following we formally extend the range of formula_15 to formula_16 with the convention that formula_17 is the operator norm.