An invariant subspace of a linear operator 
on a vector
space is a linear subspace 
such that 
. For a bounded
operator on a Hilbert space, the invariant
subspace problem concerns closed subspaces
other than 
and the whole space. If 
is the orthogonal projection
onto a closed subspace,
invariance is equivalent to
 |
A hyperinvariant subspace must instead be invariant under every operator in the commutant
of 
.
