Definition:Compact Linear Operator

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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