A characterization of singular packing subspaces with an application to limit-periodic operators

Abstract

A new characterization of the singular packing subspaces of general bounded self-adjoint operators is presented, which is used to show that the set of operators whose spectral measures have upper packing dimension equal to one is a $G_{\delta }$ (in suitable metric spaces). As an application, it is proven that, generically (in space of continuous sampling functions), spectral measures of the limit-periodic Schrödinger operators have upper packing dimensions equal to one. Consequently, in a generic set, these operators are quasiballistic.

Accepted for publication in Forum Mathematicum