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

摘要

The Dirac operatorswith L2-potentialsconsidered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projectionsare well-defined for |n | ≥ N if N is sufficiently large. It is proved thatwhere P0_n, n ∈ ℤ, are the Riesz projections of the free operator.Then, by the Bari–Markus criterion, the spectral Riesz decompositionsconverge unconditionally in L2 (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)