Regularity Properties of Sectorial Operators: Counterexamples and Open Problems

TL;DR

This paper surveys the regularity properties of sectorial operators on Banach spaces, highlighting key results, open problems, and methods for constructing counterexamples to deepen understanding in the field.

Contribution

It provides a comprehensive overview of regularity properties, summarizes main results and open questions, and discusses techniques for constructing counterexamples in sectorial operator theory.

Findings

Summary of main regularity properties and results

Identification of open problems in the field

Methods for constructing counterexamples

Abstract

We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples.