  The methods of "minimal vectors" were introduced by Ansari and Enflo and
strengthened by Pearcy, in order to prove the existence of hyperinvariant
subspaces for certain operators on Hilbert space. In this note we present the
method of minimal vectors for operators on super-reflexive Banach spaces and we
give a new sufficient condition for the existence of hyperinvariant subspaces
of certain operators on these spaces.
