TY  - JOUR
ID  - Malejki2021
LB  - Malejki2021
AU  - Malejki, Maria
TI  - Discrete spectra for some complex infinite band matrices
ST  - Discrete spectra for some complex infinite band matrices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 6
SP  - 861
EP  - 879
DO  - https://doi.org/10.7494/OpMath.2021.41.6.861
UR  - https://doi.org/10.7494/OpMath.2021.41.6.861
AB  - Under suitable assumptions the eigenvalues for an unbounded discrete operator \(A\) in \(l_2\), given by an infinite complex band-type matrix, are approximated by the eigenvalues of its orthogonal truncations. Let \[\Lambda (A)=\{\lambda \in {\rm Lim}_{n\to \infty} \lambda _n : \lambda _n \text{ is an eigenvalue of } A_n \text{ for } n \geq 1 \},\] where \({\rm Lim}_{n\to \infty} \lambda_n\) is the set of all limit points of the sequence \((\lambda_n)\) and \(A_n\) is a finite dimensional orthogonal truncation of \(A\). The aim of this article is to provide the conditions that are sufficient for the relations \(\sigma(A) \subset \Lambda(A)\) or \(\Lambda (A) \subset \sigma (A)\) to be satisfied for the band operator \(A\).
KW  - unbounded operator
KW  - band-type matrix
KW  - complex tridiagonal matrix
KW  - discrete spectrum
KW  - eigenvalue
KW  - limit points of eigenvalues
SN  - 1232-9274
ER  -