Extremal vectors and rectifiability

  • Per Enflo
  • Aderaw Fenta

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.

Quaestiones Mathematicae 34(2011), 119-123

Author Biographies

Per Enflo
Department of Mathematical Sciences, Kent State University, Summit Street, Kent OH 44242
Aderaw Fenta
Department of Mathematical Sciences, Kent State University, Summit Street, Kent OH 44242
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606