# Reference request on operators with compact powers

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.

• 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. – Conifold Mar 5 at 20:09
• @Conifold thank you for the useful information! – Mathsira Mar 5 at 20:34