Let $T$ be a compact operator and suppose $M$ is an invariant subspace for $T$. I need to show that $T|_M$ is compact.
Any hint on how to begin with this problem?
2026-03-27 19:30:55.1774639855
Show $T|_{M}$ is a compact operator
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$T$ (defined on $X$) is compact is equivalent to saying that the image of the unit ball is contained in a compact set. The unit ball of $M$ is a closed subset of the unit ball of $X$, so the adherence of its image is contained in the adherence of the image of the unit ball of $X$ so it is compact.