Convergence properties of minimal vectors for normal operators and weighted shifts

We study the behaviour of the sequence of minimal vectors corresponding to certain classes of operators on reflexive spaces, including multiplication operators and bilateral weighted shifts. The results proved are based on explicit formulae for the minimal vectors, and provide extensions of results due to Ansari and Enflo, and also Wiesner. In many cases the convergence of sequences associated with the minimal vectors leads to the construction of hyperinvariant subspaces for cyclic operators.