An infinite-dimensional generalization of Zenger's lemma

TL;DR

This paper extends Zenger's lemma to infinite-dimensional spaces, providing new theoretical tools with potential applications in economic models and operator theory.

Contribution

It presents the first infinite-dimensional generalization of Zenger's lemma, expanding its applicability in functional analysis and economic modeling.

Findings

Generalization of Zenger's lemma to infinite dimensions

Examples illustrating the lemma's application

Discussion of potential use in Arrow-Debreu model

Abstract

We prove an infinite-dimensional generalization of Zenger's lemma that was used in the proof of the fact that the convex hull of the point spectrum of a linear operator is contained in its numerical range. Two relevant examples are given, and possible application in the Arrow-Debreu model is also discussed.