Definition:Compact Linear Operator

Definition

Normed Vector Space

Let $\struct {X, \norm \cdot}$ be a normed vector space.

Let $T : X \to X$ be a compact linear transformation.

We say that $T$ is a compact linear operator.

Inner Product Space

Let $\struct {X, \innerprod \cdot \cdot}$ be an inner product space.

Let $T : X \to X$ be a compact linear transformation.

We say that $T$ is a compact linear operator.

Also see

• Definition:Compact Linear Transformation