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Surjective maps preserving quasi-nilpotence of products of operators
Let $X$ be an infinite-dimensional complex Banach space and let $\mathcal B(X)$ the full algebra of all bounded linear operator on $X$. In this paper, we give a complete characterization of surjective maps $ϕ:\mathcal B(X)\to\mathcal B(X)$ satisfying \[ r(AB)=0\quad\Longleftrightarrow\quad r(ϕ(A)ϕ(B
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