AbstractThe Dirac operators equation image with L2‐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 P0 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 L2 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)