The spectral singularities of injective weighted shifts (Q1174421)

From the Introduction: ``The set of spectral singularities in the strict sense \(S_ 2(T)\) will be defined here as the smallest set ... `outside which' \(T\) behaves like a spectral operator of scalar type. Using the basic result of R. Geller and the survey of A. Shield, in this note we determine these sets for the injective unilateral and bilateral weighted shifts on the spaces \(\ell^ 2(\mathbb{N})\) and \(\ell_ 2(\mathbb{Z})\), respectively (\(\mathbb{N}\), \(\mathbb{Z}\) and \(\mathbb{C}\) will denote the set of all positive integers, integers and complex numbers respectively).''.