# Spectrum of Weighted Composition Operators. Part V. Spectrum and essential spectra of weighted rotation-like operators

## TL;DR

This paper introduces weighted rotation-like operators, explores their essential spectra, and provides detailed descriptions of these spectra for weighted rotation operators in Banach spaces of measurable and analytic functions.

## Contribution

It defines a new class of weighted rotation-like operators and analyzes their essential spectra, offering comprehensive spectral descriptions in specific Banach spaces.

## Key findings

- Characterization of essential spectra of weighted rotation-like operators
- Complete descriptions of spectra for weighted rotation operators in certain Banach spaces
- Development of a framework for spectral analysis of rotation-like operators

## Abstract

We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted rotation operators in Banach spaces of measurable and analytic functions.