Extremal vectors and rectifiability

Abstract

The concept of extremal vectors of a linear operator with a dense range but not onto on a Hilbert space was introduced by P. Enflo in 1996 as a new approach to study invariant subspaces. Following this, there were several studies on analytic and geometric properties of backward minimal vectors and their applications to construction of invariant subspaces. In this paper, we consider one other property: rectifiability. We show that in general curves that map numbers to backward minimal vectors are not rectifiable.