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