On the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range

TL;DR

This paper explores elliptical range theorems for the Davis-Wielandt shell, numerical range, and conformal range, focusing on elementary methods and quadratic representations to deepen understanding of these spectral sets.

Contribution

It introduces new elementary approaches to analyze elliptical range theorems for various spectral sets using quadratic representations.

Findings

Elliptical range theorems are characterized for Davis-Wielandt shell, numerical range, and conformal range.

Elementary methods provide new insights into the structure of these spectral sets.

Quadratic representations are effective tools for analyzing the elliptical properties of these ranges.

Abstract

We consider the elliptical range theorems for the Davis--Wielandt shell, the numerical range, and the conformal range in terms of and related to their quadratic representations. The emphasis is on exposing a variety of elementary approaches.