The following is an exercise of Conway's operator theory: 
I proved all parts of this exercise except $\|KT_n\| \to 0$. I can easily prove $\|KT_n^*\|\to 0$, but do not have any idea to prove $\|KT_n\| \to 0$. Plase give me a hint. Thanks.
2026-03-28 20:13:33.1774728813
Compact operator and a sot convergent sequence of operators
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