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.