On the Riesz Inequality and the Basis Property of Systems of Root Vector Functions of a Discontinuous Dirac Operator

Abstract

We consider a discontinuous Dirac operator on the interval (0, 2π). It is assumed that its coefficient (potential) is a complex-valued matrix function integrable on (0, 2π). Criteria are established for the Riesz and unconditional basis properties of the system of root vector functions in L 2 2 (0, 2π). A theorem about the equivalent basis property in L 2 (0, 2π), 1 ∞, is proved.