Fredholm operator

A Fredholm operator is a specific type of bounded linear operator that arises in functional analysis, particularly in the study of integral and differential equations. It is defined on a Hilbert space (or a Banach space) and has certain important characteristics related to its kernel, range, and index. ### Definition: Let \( X \) and \( Y \) be Banach spaces, and let \( T: X \to Y \) be a bounded linear operator.