Definition:Fredholm Operator

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Definition

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

where:

$\map \ker T$ denotes the kernel of $T$
$\Img T$ denotes the image of $T$.


Also known as

A Fredholm operator is also known as a linear transform of finite index.


Also see

  • Results about Fredholm operators can be found here.


Source of Name

This entry was named for Erik Ivar Fredholm.


Sources