Geometry of spectral bounds of curves of unitary operators

TL;DR

This paper introduces a novel geometric approach to establish spectral bounds for products of unitary operators and extends these bounds to differentiable operator curves, enhancing understanding of their spectral behavior.

Contribution

It provides a new proof and generalization of spectral bounds for unitary operator products using metric geometric methods.

Findings

New proof of spectral bounds for unitary operator products

Generalization to differentiable curves of unitary operators

Application of metric geometry in operator spectral analysis

Abstract

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group of unitary operators and the sphere where these operators act.