  Entanglement is defined for each vector subspace of the tensor product of two
finite-dimensional Hilbert spaces, by applying the notion of operator
entanglement to the projection operator onto that subspace. The operator
Schmidt decomposition of the projection operator defines a string of Schmidt
coefficients for each subspace, and this string is assumed to characterize the
entanglement of the subspace, so that a first subspace is more entangled than a
second, if the Schmidt string of the second subspace majorizes the Schmidt
string of the first. The idea is applied to the antisymmetric and symmetric
tensor products of a finite-dimensional Hilbert space with itself, and also to
the tensor product of an angular momentum j with a spin 1/2. When adapted to
the subspaces of states of the nonrelativistic hydrogen atom with definite
total angular momentum (orbital plus spin), within the space of bound states
with a given total energy, this leads to a complete ordering of those subspaces
by their Schmidt strings.
