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In this Wikipedia page about compact operators at the very bottom it says:"If $B$ is an operator on a Banach space X such that $B^n$ is compact for some $n$, then the theorem proven above also holds for $B$."

I tried to find textbook or lecture notes to study such operators. But couldn't. Can someone help me to find a good reference? Thank you.

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    $\begingroup$ They are known as power compact or quasi-compact operators, and covered in the first volume of Dunford-Schwarz Linear Operators, p.579-80, from where even the Wikipedia's wording is lifted. $\endgroup$ – Conifold Mar 5 at 20:09
  • $\begingroup$ @Conifold thank you for the useful information! $\endgroup$ – Mathsira Mar 5 at 20:34

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