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Discrete spectra for some complex infinite band matrices

Malejki Maria

Opuscula Mathematica

2021

Vol. 41, no. 6

861--879

Under suitable assumptions the eigenvalues for an unbounded discrete operator A in l2 , given by an infinite complex band-type matrix, are approximated by the eigenvalues of its orthogonal truncations. Let [formula] where [formula] is the set of all limit points of the sequence (λn) and An is a finite dimensional orthogonal truncation of A. The aim of this article is to provide the conditions that are sufficient for the relations σ (A) ⊂ Λ (A) or Λ(A) ) ⊂ σ (A) to be satisfied for the band operator A.

Asymptotics of the discrete spectrum for complex Jacobi matrices

Malejki M.

Opuscula Mathematica

2014

Vol. 34, no. 1

139--160

The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of infinite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in l2(N).