On spectral properties of weighted shift operatorsgenerated by linear mappings

Authors: A. Antonevich, A. Akhmatova

Keywords: weighted shift operators; spectrum; one-sided invertibility; invariant measure; decomposition of oriented graph

Abstract:

Weighted shift operators B in the space L2(Cm) generated by a linear mapping A : Cm → Cm are considered. A description of properties of B − λI for λ belonging to spectrum Σ(B) is given. In particular, a necessary and sufficient condition for B − λI to be one-sided invertible is obtained.