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We consider the non-normal periodic Jacobi operator and the discrete versionsof the well-known Borg's Theorem. In this article, we extend the stabilityresults obtained recently to non-normal cases. The existing stability resultsconnect the oscillations of the matrix entries and the spectral gap size. Ourresult covers the present self-adjoint versions of Borg's theorem and itsrecent quantitative versions. Here the oscillations of the matrix entries arelinked with the path-connectedness of the pseudospectrum. We discuss the finitedifference approximations of various linear differential equations as specificapplications.

On Stability in the Borg's Theorem for Non-normal Periodic Jacobi Operators