Approximation in reflexive Banach spaces and applications to the invariant subspace problem

Abstract

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented—the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vectors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo.