Compact linear relations and their spectral properties

TL;DR

This paper investigates the spectral properties of compact linear relations, showing that their spectrum consists solely of eigenvalues and possibly zero, under certain conditions.

Contribution

It introduces new results characterizing the spectrum of compact linear relations, extending classical spectral theory to this broader context.

Findings

Spectrum of compact linear relations includes only eigenvalues and zero.

Under certain conditions, the spectrum is fully characterized.

Provides theoretical foundation for future spectral analysis of linear relations.

Abstract

In this paper, we study compact linear relations and establish that the spectrum of compact linear relations consists of only the point spectrum and the zero set under suitable conditions.