In the paper we study one-dimensional Dirac operator Dy = By + P(x)y, y = (y 1 , y 2) T , where B = 0 1 −1 0 , P(x) = diag(p(x),q(x)) , p(x) and q(x) are complex valued functions from the class L 1 (G) , G = (0,2π). Necessary and sufficient conditions of Bessel property and unconditional basicity (the Riesz basicity) of the system of root-functions of the operator D in L 2 2 (G) are set up. A theorem on equivalent basicity for these systems in L 2 2 (G) is proved.
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