A characterization of unbounded Fredholm operators

TL;DR

This paper extends the theory of Fredholm operators to unbounded cases, providing simplified and accessible arguments for a broader mathematical audience.

Contribution

It offers a characterization of unbounded Fredholm operators, building upon previous work on bounded operators and making the theory more approachable.

Findings

Provides a new characterization of unbounded Fredholm operators

Simplifies the existing theory with concise arguments

Extends the applicability of Fredholm theory to unbounded operators

Abstract

This paper is a continuation of the paper (A.G.Ramm, Amer. Math. Monthly, 108, N 9, (2001), 855-860), where bounded Fredholm operators are studied. The theory of bounded linear Fredholm-type operators is presented in many texts. This paper is written for a broad audience and the author tries to give simple and short arguments.