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Keywords:
Kleinecke-Shirokov theorem; generalized commutator
Kleinecke-Shirokov theorem; generalized commutator
Summary:
We prove that for normal operators $N_1, N_2\in \mathcal {L(H)},$ the generalized commutator $[N_1, N_2; X]$ approaches zero when $[N_1,N_2; [N_1, N_2; X]]$ tends to zero in the norm of the Schatten-von Neumann class $\mathcal {C}_p$ with $p>1$ and $X$ varies in a bounded set of such a class.
References:
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