Abstract Weyl-type Theorems

TL;DR

This paper introduces a new framework for analyzing Weyl-type theorems using spectral valued functions and order relations, simplifying the understanding of their relationships and deriving known results as corollaries.

Contribution

It proposes spectral valued and partitioning functions, and a novel order-based approach to study Weyl-type theorems, unifying and extending previous results.

Findings

Complete characterization of relationships between spectral valued functions.

Reduction of Weyl-type theorem relationships to set differences in spectra.

Derivation of known results as corollaries of the new framework.

Abstract

In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued functions, we reduce the question of relationship between Weyl-type theorems to the study of the set difference between the parts of the spectrum that are involved. This study solves completely the question of relationship between two spectral valued functions, comparable for one or the other order relation. Then several known results about Weyl-type theorems becomes corollaries of the results obtained.