Essential spectrum of a limit of self--adjoint operators

TL;DR

This paper derives a formula relating the essential spectrum of a limit of self-adjoint operators to the essential spectra of the sequence elements, assuming norm resolvent convergence.

Contribution

It provides a new formula connecting the essential spectrum of the limit operator with those of the sequence elements under norm resolvent convergence.

Findings

Established a formula for the essential spectrum of the limit operator.

Linked the essential spectrum of the limit to that of the sequence elements.

Enhanced understanding of spectral behavior under operator limits.

Abstract

For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.