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Journal of Operator Theory

Volume 67, Issue 1, Winter 2012  pp. 237-256.

Weyl sequences and the essential spectrum of some Jacobi operators

Authors:  Marcin Moszynski
Author institution: Wydzial Matematyki Informatyki i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland

Summary:  This work is devoted to finding Weyl sequences for some Jacobi operators and, consequently, describing some of the essential spectra subsets. In particular we study those problems for perturbations of the Jacobi operators with the $k$-th weight given by $k^{\al}$ or by $k^{\al}+b_k$, where $\al\in(0;1)$ and $\sse{b_k}$ is a $2$-periodic sequence.

Keywords:  Jacobi matrix (operator), spectrum, essential spectrum, approximative spectrum, Weyl sequence, perturbations

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