A Fredholm operator is a bounded linear operator between Banach spaces whose kernel
and cokernel are finite-dimensional
and whose range is a closed set.
Its index is 
and is unchanged when a compact operator is added.
Fredholm Operator
See also
Banach Space, Compact Operator, Null Space, OperatorExplore with Wolfram|Alpha
References
Conway, J. B. A Course in Functional Analysis, 2nd ed. New York: Springer-Verlag, 1990.Cite this as:
Weisstein, Eric W. "Fredholm Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FredholmOperator.html