6 Unbounded Fredholm operators
Nora Doll, Hermann Schulz‐Baldes, Nils Waterstraat · 2023
Unbounded Fredholm operatorsThis chapter offers a detailed introduction to various subsets of the unbounded Fredholm operators, with a particular focus on natural topologies thereon.This is a necessary preparation for the definition of spectral flow of unbounded self-adjoint Fredholm operators given in the next Chapter 7. First, Section 6.1 reviews various topologies on the set of closed operators.Section 6.2 recalls some fundamentals about unbounded Fredholm operators that can be found in numerous books, e. g., [80, 99, 165].Then, following the works of Lesch, and Phillips [31], as well as Lesch [126], the set of unbounded self-adjoint Fredholm operators and its topology is studied in detail in Section 6.3.Section 6.4 considers the important subclass of self-adjoint Fredholm operators with compact resolvent and proves numerous topological results.