Compact Linear Transformation is Bounded
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This theorem requires a proof..
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Theorem
Let $H, K$ be Hilbert spaces.
Let $T \in \map {B_0} {H, K}$ be a compact linear transformation.
Then $T$ is also a bounded linear transformation.
That is:
- $\map {B_0} {H, K} \subseteq \map B {H, K}$
Proof
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Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $\text {II}.4.2 \ \text {(a)}$