Bari–Markus property for Riesz projections of 1D periodic Dirac operators

Abstract

Abstract The Dirac operators equation image with L 2 ‐potentials equation image considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions ( bc ), have discrete spectra, and the Riesz projections equation image are well‐defined for | n | ≥ N if N is sufficiently large. It is proved that equation image where P 0 n , n ∈ ℤ, are the Riesz projections of the free operator. Then, by the Bari–Markus criterion, the spectral Riesz decompositions equation image converge unconditionally in L 2 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)