Fredholmoperátorokat
Fredholmoperátorok, sometimes referred to as Fredholm operators, are a class of linear operators between Banach spaces that are fundamental in functional analysis and have significant applications in the study of differential equations and index theory. An operator T from a Banach space X to a Banach space Y is called a Fredholm operator if it satisfies three conditions: its kernel (null space) is finite-dimensional, its image (range) is closed, and the codimension of its image is finite-dimensional. The codimension of the image of T is defined as the dimension of the quotient space Y/Im(T).
The key property of Fredholm operators is their index. The index of a Fredholm operator T is
Fredholm operators are also characterized by the fact that they are exactly the operators for which there