On the spectra of tridiagonal non-symmetric matrices

Abstract

A study is made of the spectra of infinite tridiagonal matrices as operators on the Hahn sequence space h and the space ${\mathrm{bv}}_0$ of null sequences of bounded variation. The study includes: the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the considered matrices. It is shown that the method used in this paper is suitable also for determining the spectra of triangular double-band matrices and the Jacobi matrices.