Article

On the number of components of the essential spectrum of one 2х2 operator matrix

M. I. MuminovSamarkand State University,I. N. BozorovV.I. Romanovsky Institute of Mathematics of the Academy of Sciences of UzbekistanTulkin H. RasulovBukhara State University

Izvestiya Vysshikh Uchebnykh Zavedenii Matematikajournal2024en

ABI

Abstract

In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σ ess (H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σ ess (H) are singled out. We prove that the essential spectrum σ ess (H) consists of no more than six segments (components).

Topics

Matrix Theory and Algorithms Holomorphic and Operator Theory Mathematical Analysis and Transform Methods

Identifiers

DOI: 10.26907/0021-3446-2024-2-85-90

Citations and references

Cited by 3 7 references

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