Compact Perturbations of Fredholm n-tuples II

TL;DR

This paper explores specific Fredholm n-tuples of operators with index 0 that cannot be adjusted to have an exact Koszul complex through compact perturbations, highlighting limitations in perturbation theory.

Contribution

It provides examples of Fredholm n-tuples with index 0 that resist compact perturbations to achieve an exact Koszul complex, advancing understanding of operator perturbations.

Findings

Examples of Fredholm n-tuples with index 0 that cannot be perturbed to exact complexes

Demonstrates limitations of compact perturbations in operator theory

Highlights the need for alternative approaches in perturbation analysis

Abstract

The paper contains examples of Fredholm n-tuples of operators that are of index 0 but cannot be perturbed by compact operators to n-tuples with exact Koszul complex.