Category:Definitions/Fredholm Operators

This category contains definitions related to Fredholm Operators.
Related results can be found in Category:Fredholm Operators.

Let $U, V$ be vector spaces.

Let $T: U \to V$ be a linear transformation.

$T$ is a Fredholm operator if and only if:

$(1): \quad \map \ker T$ is finite-dimensional

$(2): \quad$ the quotient space $V / \Img T$ is finite-dimensional