Operator space analogues of locally convex spaces
 
  Local operator spaces are defined to be projective limits of
  operator spaces, and they may be regarded as the "quantized" or
  "operator" analogues of locally convex spaces.  In a striking contrast
  to normed spaces we will show that nuclear locally convex spaces have
  precisely one local operator space structure. Furthermore, we show that
  a local operator space is nuclear in the operator sense if and only if
  the underlying locally convex space is nuclear.