Compact Linear Transformations Composed with Bounded Linear Operator
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Theorem
Let $H, K$ be Hilbert spaces.
Let $T \in B_0 \left({H, K}\right)$ be a compact linear transformation.
Let $A \in B \left({H}\right), B \in B \left({K}\right)$ be bounded linear operators.
Then the compositions $TA$ and $BT$ are also compact linear transformations.
Proof
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Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.4.2(c)$